Journal of Functional Analysis最新文献

英文中文

Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle 具有小体积障碍的狄利克雷拉普拉斯算子的第一特征值的最小化

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-21 DOI: 10.1016/j.jfa.2026.111362

Benedetta Noris , Giovanni Siclari , Gianmaria Verzini

We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains Ω having prescribed volume and contained in a fixed box D; equivalently, we look for the best way to remove a compact set (obstacle)

K \subset \overline{D}

of Lebesgue measure

| K | = ε

0 < ε < | D |

, in order to minimize the first Dirichlet eigenvalue of the set

Ω = D ∖ K

In the small volume regime

ε \to 0

, we prove that the optimal obstacles accumulate, in a suitable sense, to points of ∂D where

| \nabla ϕ_{0} |

is minimal, where

ϕ_{0}

denotes the first eigenfunction of the Dirichlet Laplacian on D. Moreover, we provide a fairly detailed description of the convergence of the optimal eigenvalues, eigenfunctions and free boundaries. Our results are based on sharp estimates of the optimal eigenvalues, in terms of a suitable notion of relative capacity.

我们考虑了众所周知的具有谱代价的形状优化问题：在所有具有规定体积且包含在固定框D中的子域Ω中，最小化狄利克雷拉普拉斯算子的第一个特征值；同样地，我们寻找移除Lebesgue测度|K bb b1 =ε, 0<ε<；|D bb b3的紧集（障碍）K∧D的最佳方法，以最小化集合Ω=D≠K的第一个Dirichlet特征值。在小体积区域ε→0中，我们证明了在适当的意义上，最优障碍累积到∂D的点，其中|∇ϕ0|最小，其中ϕ0表示D上的Dirichlet拉普拉斯算子的第一个特征函数。此外，我们提供了最优特征值、特征函数和自由边界的收敛性的相当详细的描述。我们的结果是基于最优特征值的尖锐估计，在一个合适的相对容量的概念。

{"title":"Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle","authors":"Benedetta Noris , Giovanni Siclari , Gianmaria Verzini","doi":"10.1016/j.jfa.2026.111362","DOIUrl":"10.1016/j.jfa.2026.111362","url":null,"abstract":"<div><div>We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains Ω having prescribed volume and contained in a fixed box <em>D</em>; equivalently, we look for the best way to remove a compact set (obstacle) <span><math><mi>K</mi><mo>⊂</mo><mover><mrow><mi>D</mi></mrow><mo>‾</mo></mover></math></span> of Lebesgue measure <span><math><mo>|</mo><mi>K</mi><mo>|</mo><mo>=</mo><mi>ε</mi></math></span>, <span><math><mn>0</mn><mo><</mo><mi>ε</mi><mo><</mo><mo>|</mo><mi>D</mi><mo>|</mo></math></span>, in order to minimize the first Dirichlet eigenvalue of the set <span><math><mi>Ω</mi><mo>=</mo><mi>D</mi><mo>∖</mo><mi>K</mi></math></span>.</div><div>In the small volume regime <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, we prove that the optimal obstacles accumulate, in a suitable sense, to points of ∂<em>D</em> where <span><math><mo>|</mo><mi>∇</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>|</mo></math></span> is minimal, where <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> denotes the first eigenfunction of the Dirichlet Laplacian on <em>D</em>. Moreover, we provide a fairly detailed description of the convergence of the optimal eigenvalues, eigenfunctions and free boundaries. Our results are based on sharp estimates of the optimal eigenvalues, in terms of a suitable notion of relative capacity.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111362"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Half-space Liouville-type theorems for minimal graphs with capillary boundary 具有毛细边界的极小图的半空间liouville型定理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-21 DOI: 10.1016/j.jfa.2026.111366

Guofang Wang , Wei Wei , Xuwen Zhang

In this paper, we prove two Liouville-type theorems for capillary minimal graph over

R_{+}^{n}

. First, if u has linear growth, then for

n = 2, 3

and for any

θ \in (0, π)

, or

n \geq 4

and

θ \in (\frac{π}{6}, \frac{5 π}{6})

, u must be flat. Second, if u is one-sided bounded on

R_{+}^{n}

, then for any n and

θ \in (0, π)

, u must be flat. The proofs build upon gradient estimates for the mean curvature equation over

R_{+}^{n}

with capillary boundary condition, which are based on carefully adapting the maximum principle to the capillary setting.

本文证明了R+n上毛细极小图的两个liouville型定理。首先，如果u具有线性增长，则对于n=2,3，对于任意θ∈(0,π)，或n≥4且θ∈(π6,5π6)， u必须是平坦的。第二，如果u在R+n上是单侧有界的，那么对于任意n和θ∈(0,π)， u一定是平的。这些证明建立在具有毛细管边界条件的R+n上的平均曲率方程的梯度估计的基础上，该梯度估计是基于仔细地将极大值原理应用于毛细管设置。

引用次数: 0

On the log-Sobolev constant of log-concave vectors 关于log-Sobolev常数的对数凹向量

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-21 DOI: 10.1016/j.jfa.2026.111368

Pierre Bizeul

It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases.

众所周知，如果一个随机向量满足log-Sobolev不等式，它的所有边际都有亚高斯尾。在KLS猜想的精神下，我们研究了在对数凹性假设下是否可以反转这一含义。在一般情况下，我们改进了Bobkov的结果，建立了亚高斯对数凹测度的log-Sobolev常数的最佳维数依赖界，并研究了一些特殊情况。

引用次数: 0

Maximality and symmetry related to the 2-adic ring C⁎-algebra 二进环C -代数的极大性和对称性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-21 DOI: 10.1016/j.jfa.2026.111349

Dolapo Oyetunbi, Dilian Yang

The 2-adic ring

C^{⁎}

-algebra

Q_{2}

is the universal

C^{⁎}

-algebra generated by a unitary and an isometry satisfying certain relations. It contains a canonical copy of the Cuntz algebra

O_{2}

. We show that

O_{2}

is a maximal

C^{⁎}

-subalgebra of

Q_{2}

. Furthermore, we examine the structure of the fixed-point algebra under a periodic ^⁎-automorphism σ of

Q_{2}

, which is extended from the flip-flop ^⁎-automorphism of

O_{2}

. We show that the maximality of

O_{2}

Q_{2}

extends to the crossed product

O_{2} ⋊_{σ} Z_{2}

Q_{2} ⋊_{σ} Z_{2}

, and to the fixed-point algebra

O_{2}^{σ}

Q_{2}^{σ}

. As a consequences of our main results, a few open questions concerning

Q_{2}

are resolved.

二进环C -代数Q2是由满足一定关系的酉和等距生成的全称C -代数。它包含了昆兹代数O2的一个规范副本。我们证明O2是Q2的一个极大C - C -子代数。进一步，我们研究了由O2的触发器式的自同构推广而来的Q2的周期式的 -自同构σ下的不动点代数的结构。我们证明了Q2中O2的极大值可以扩展到Q2中O2的交叉积O2的∑z2，以及Q2中O2的不动代数O2的不动代数。由于我们的主要结果，一些关于Q2的开放问题得到了解决。

引用次数: 0

Complete asymptotic analysis of low energy scattering for Schrödinger operators with a short-range potential 具有近程势的Schrödinger算子的低能量散射的完全渐近分析

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-14 DOI: 10.1016/j.jfa.2026.111345

Ethan Sussman

Recent work by Hintz–Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension

d \geq 3

, for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein–Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible.

Hintz-Vasy最近的工作提供了对具有短程势的Schrödinger算符的低能量散射极限的部分渐近分析。利用对Hintz算法的稍微改进，我们通过在每一个可能的渐近区域中提供完整的渐近展开式来完成渐近分析。此外，对任意d≥3维的渐近二次流形进行了分析，并跟踪了部分多极展开。应用包括Schrödinger，波和Klein-Gordon方程的完全渐近分析，其中一个在同伴论文中被描述。使用以前的工作，只有部分渐近分析是可能的。

引用次数: 0

Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term 具有奇异非齐次项的分数阶半线性热方程解的存在性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111352

Kazuhiro Ishige , Tatsuki Kawakami , Ryo Takada

We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term.

研究了一类具有奇异非齐次项的分数阶半线性热方程解的存在性。为此，我们建立了若干一致局部Zygumnd空间中分数阶热半群的衰减估计。进一步，我们在一致局部Zygmund空间中应用实插值方法，得到了非齐次项和非线性项的尖锐积分估计。这使我们能够找到具有奇异非齐次项的分数阶半线性热方程解存在的充分条件。

引用次数: 0

Global well-posedness and density patches for liquid crystal system 液晶系统的全局适定性和密度补丁

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111356

Qionglei Chen , Xiaonan Hao , Omar Lazar

We prove a global well-posedness result for a liquid crystal system with bounded but arbitrarily large density and velocity. Applying the Lagrangian approach with more refined estimates we are able to not only work in the critical regularity space but also to overcome the difficulty arising from the fact that we are dealing with a coupled hyperbolic system. Taking advantage of our uniqueness result, we study the density patches problem by using classical techniques, namely, Littlewood-Paley multipliers together with the smoothing effect of the Newtonian potential and on certain symmetry property motivated by [13]. One of the key point of the proof is to introduce the material derivative and perform more refined estimates for the direction field.

我们证明了具有有界但任意大密度和速度的液晶系统的全局适定性结果。应用拉格朗日方法和更精细的估计，我们不仅能够在临界正则性空间中工作，而且能够克服由于我们处理耦合双曲系统而产生的困难。利用我们的唯一性结果，我们利用经典的方法，即Littlewood-Paley乘法器，结合牛顿势的平滑效应，以及[13]驱动下的某种对称性，研究了密度斑块问题。证明的关键之一是引入物质导数，对方向场进行更精细的估计。

引用次数: 0

On von Neumann algebras generated by free Poisson random weights 自由泊松随机权生成的von Neumann代数

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111358

Zhiyuan Yang

We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight φ on a von Neumann algebra M. We give an explicit construction of the free Poisson random weight using full Fock space over the Hilbert space

L^{2} (M, φ)

and study the free Poisson von Neumann algebra

Γ (M, φ)

generated by this random weight. This construction can be viewed as a free Poisson type functor for left Hilbert algebras similar to Voiculescu's free Gaussian functor for Hilbert spaces. When

φ (1) < \infty

, we show that

Γ (M, φ)

can be decomposed into free product of other algebras. For a general weight φ, we prove that

Γ (M, φ)

is a factor if and only if

φ (1) \geq 1

and

M \neq C

. The second quantization of subunital weight decreasing completely positive maps is studied. By considering a degenerate version of left Hilbert algebras, we are also able to treat free Araki-Woods algebras as special cases of free Poisson algebras for degenerate left Hilbert algebras. We show that the Lévy-Itô decomposition of a jointly freely infinitely divisible family (in a tracial probability space) can in fact be interpreted as a decomposition of a degenerate left Hilbert algebra. Finally, as an application, we give a realization of any additive time-parameterized free Lévy process as unbounded operators in a full Fock space. Using this realization, we show that the filtration algebras of any additive free Lévy process are always interpolated group factors with a possible additional atom.

在Hilbert空间L2（M,φ）上利用满Fock空间给出了自由泊松随机权的显式构造，并研究了由该随机权生成的自由泊松von Neumann代数Γ（M,φ）。这种构造可以看作是左希尔伯特代数的自由泊松型函子，类似于Voiculescu的希尔伯特空间的自由高斯函子。当φ(1)<；∞时，我们证明Γ（M,φ）可以分解为其它代数的自由积。对于一般权值φ，证明Γ（M,φ）是因子当且仅当φ(1)≥1且M≠C。研究了亚单位权递减完全正映射的二次量化问题。通过考虑左希尔伯特代数的退化版本，我们也能够将自由Araki-Woods代数视为退化左希尔伯特代数的自由泊松代数的特殊情况。我们证明了联合自由无限可分族（在迹概率空间中）的Lévy-Itô分解实际上可以解释为退化的左希尔伯特代数的分解。最后，作为应用，我们给出了在满Fock空间中任意加性时参数化自由lsamvy过程作为无界算子的实现。利用这一实现，我们证明了任何可加自由lsamvy过程的过滤代数都是内插的群因子，并可能有一个额外的原子。

{"title":"On von Neumann algebras generated by free Poisson random weights","authors":"Zhiyuan Yang","doi":"10.1016/j.jfa.2026.111358","DOIUrl":"10.1016/j.jfa.2026.111358","url":null,"abstract":"<div><div>We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight <em>φ</em> on a von Neumann algebra <em>M</em>. We give an explicit construction of the free Poisson random weight using full Fock space over the Hilbert space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> and study the free Poisson von Neumann algebra <span><math><mi>Γ</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> generated by this random weight. This construction can be viewed as a free Poisson type functor for left Hilbert algebras similar to Voiculescu's free Gaussian functor for Hilbert spaces. When <span><math><mi>φ</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo><</mo><mo>∞</mo></math></span>, we show that <span><math><mi>Γ</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> can be decomposed into free product of other algebras. For a general weight <em>φ</em>, we prove that <span><math><mi>Γ</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> is a factor if and only if <span><math><mi>φ</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>≥</mo><mn>1</mn></math></span> and <span><math><mi>M</mi><mo>≠</mo><mi>C</mi></math></span>. The second quantization of subunital weight decreasing completely positive maps is studied. By considering a degenerate version of left Hilbert algebras, we are also able to treat free Araki-Woods algebras as special cases of free Poisson algebras for degenerate left Hilbert algebras. We show that the Lévy-Itô decomposition of a jointly freely infinitely divisible family (in a tracial probability space) can in fact be interpreted as a decomposition of a degenerate left Hilbert algebra. Finally, as an application, we give a realization of any additive time-parameterized free Lévy process as unbounded operators in a full Fock space. Using this realization, we show that the filtration algebras of any additive free Lévy process are always interpolated group factors with a possible additional atom.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111358"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Landau damping and survival threshold 朗道阻尼和生存阈值

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111357

Toan T. Nguyen

In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogeneous equilibria

μ (\frac{1}{2} | v |^{2})

with connected support on the torus

T_{x}^{3} \times R_{v}^{3}

or on the whole space

R_{x}^{3} \times R_{v}^{3}

, including those that are non-monotone. The problem can be solved completely mode by mode for each spatial wave number, and their longtime dynamics is intimately tied to the “survival threshold” of wave numbers computed by

κ_{0}^{2} = 4 π \int_{0}^{ϒ} \frac{u^{2} μ (\frac{1}{2} u^{2})}{ϒ^{2} - u^{2}} d u

where ϒ is the maximal speed of particle velocities. It is shown that purely oscillatory electric fields exist and obey a Klein-Gordon's type dispersion relation for wave numbers below and up to the threshold, thus rigorously confirming the existence of Langmuir's oscillatory waves for a non-trivial range of spatial frequencies in this linearized setting. At the threshold, the phase velocity of these oscillatory waves enters the range of admissible particle velocities, namely there are particles that move at the same propagation speed of the waves. It is this exact resonant interaction between particles and the oscillatory fields that causes the waves to be damped, classically known as Landau damping. Landau's law of decay is explicitly computed and is sensitive to the decaying rate of the background equilibria. The faster it decays at the maximal velocity, the weaker Landau damping is. Beyond the threshold, the electric fields are a perturbation of those generated by the free transport dynamics and thus decay rapidly fast due to the phase mixing mechanism.

本文在环面Tx3×Rv3或整个空间Rx3×Rv3上，建立了具有连通支撑的一般空间齐次平衡点μ(12|v|2)附近线性化Vlasov-Poisson系统解的大时渐近性，包括非单调的解。对于每个空间波数，这个问题可以通过一个模式一个模式地完全解决，它们的长期动态与由κ02=4π∫0ϒu2μ(12u2)ϒ2−u2du计算的波数的“生存阈值”密切相关，其中y是粒子速度的最大速度。结果表明，在阈值以下和阈值以上的波数存在纯振荡电场，且服从Klein-Gordon型色散关系，从而严格证实了在线性化条件下，在非平凡的空间频率范围内存在Langmuir振荡波。在阈值处，这些振荡波的相速度进入允许的粒子速度范围，即存在与波的传播速度相同的粒子。正是这种粒子与振荡场之间的共振相互作用导致了波的衰减，即经典的朗道阻尼。朗道衰减定律是明确计算的，并且对背景平衡态的衰减速率敏感。在最大速度下衰减越快，朗道阻尼越弱。超过阈值，电场是由自由输运动力学产生的扰动，因此由于相位混合机制而迅速衰减。

{"title":"Landau damping and survival threshold","authors":"Toan T. Nguyen","doi":"10.1016/j.jfa.2026.111357","DOIUrl":"10.1016/j.jfa.2026.111357","url":null,"abstract":"<div><div>In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogeneous equilibria <span><math><mi>μ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> with connected support on the torus <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> or on the whole space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>, including those that are non-monotone. The problem can be solved completely mode by mode for each spatial wave number, and their longtime dynamics is intimately tied to the “survival threshold” of wave numbers computed by<span><span><span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>4</mn><mi>π</mi><munderover><mo>∫</mo><mrow><mn>0</mn></mrow><mrow><mi>ϒ</mi></mrow></munderover><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>μ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><msup><mrow><mi>ϒ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mspace></mspace><mi>d</mi><mi>u</mi></math></span></span></span> where ϒ is the maximal speed of particle velocities. It is shown that purely oscillatory electric fields exist and obey a Klein-Gordon's type dispersion relation for wave numbers below and up to the threshold, thus rigorously confirming the existence of Langmuir's oscillatory waves for a non-trivial range of spatial frequencies in this linearized setting. At the threshold, the phase velocity of these oscillatory waves enters the range of admissible particle velocities, namely there are particles that move at the same propagation speed of the waves. It is this exact resonant interaction between particles and the oscillatory fields that causes the waves to be damped, classically known as Landau damping. Landau's law of decay is explicitly computed and is sensitive to the decaying rate of the background equilibria. The faster it decays at the maximal velocity, the weaker Landau damping is. Beyond the threshold, the electric fields are a perturbation of those generated by the free transport dynamics and thus decay rapidly fast due to the phase mixing mechanism.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111357"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional boundary Hardy inequality for the critical cases 临界情况下的分数边界Hardy不等式

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111351

Adimurthi, Prosenjit Roy, Vivek Sahu

We establish generalized fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of s and p on various domains in

R^{d}, d \geq 1

. In particular, for Lipschitz bounded domains any values of s and p are admissible, settling all the cases in subcritical, supercritical and critical regime. In this paper we have solved the open problems posed by Dyda for the critical case

s p = 1

. Moreover we have proved the embeddings of

W_{0}^{s, p} (Ω)

in subcritical, critical and supercritical uniformly without using Dyda's decomposition. Additionally, we extend our results to include a weighted fractional boundary Hardy-type inequality for the critical case.

根据Caffarelli-Kohn-Nirenberg不等式的精神，在Rd，d≥1的不同定域上，对s和p的不同值，建立了广义分数阶边界hardy型不等式。特别地，对于Lipschitz有界区域，s和p的任何值都是允许的，解决了在亚临界、超临界和临界区域的所有情况。在sp=1的临界情况下，我们解决了由Dyda提出的开放问题。此外，我们还在不使用Dyda分解的情况下，均匀地证明了W0s、p（Ω）在亚临界、临界和超临界中的嵌入。此外，我们扩展了我们的结果，以包含临界情况下的加权分数边界hardy型不等式。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Functional Analysis

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀