Nonlinear Analysis-Theory Methods & Applications最新文献

英文中文

One-dimensional symmetry results for semilinear equations and inequalities on half-spaces 半空间上半线性方程和不等式的一维对称结果

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.na.2025.113983

Nicolas Beuvin, Alberto Farina

We prove new one-dimensional symmetry results for non-negative solutions, possibly unbounded, to the semilinear equation

- Δ u = f (u)

in the upper half-space

R_{+}^{N}

. Some Liouville-type theorems are also proven in the case of differential inequalities in

R_{+}^{N}

, even without imposing any boundary condition.

Although subject to dimensional restrictions, our results apply to a broad family of functions

f

. In particular, they apply to all non-negative

f

that behaves at least linearly at infinity.

我们证明了半线性方程- Δu=f(u)在上半空间R+N中的非负解（可能无界）的新的一维对称性结果。对于R+N中的微分不等式，即使不施加任何边界条件，也证明了一些liouville型定理。虽然受到维度的限制，我们的结果适用于广泛的函数族f。特别是，它们适用于在无穷远处表现为线性的所有非负函数f。

引用次数: 0

Euler–Lagrange equations for variable-growth total variation 变增长总变分的欧拉-拉格朗日方程

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.na.2025.113984

Wojciech Górny , Michał Łasica , Alexandros Matsoukas

We consider a class of integral functionals with Musielak–Orlicz type variable growth, possibly linear in some regions of the domain. This includes

p (x)

power-type integrands with

p (x) \geq 1

as well as double-phase

p - q

integrands with

p = 1

. The main goal of this paper is to identify the

L^{2}

-subdifferential of the functional, including a local characterisation in terms of a variant of the Anzellotti product defined through the Young’s inequality. As an application, we obtain the Euler–Lagrange equation for the variant of Rudin–Osher–Fatemi image denoising problem with variable growth regularising term. Moreover, we provide a characterisation of the

L^{2}

-gradient flow of variable-growth total variation in terms of a parabolic PDE.

我们考虑一类具有Musielak-Orlicz型变增长的积分泛函，在某些区域可能是线性的。这包括p(x)≥1的p(x)幂型积分以及p=1的双相p−q积分。本文的主要目标是确定泛函的l2 -子微分，包括通过杨氏不等式定义的Anzellotti积的变体的局部表征。作为应用，我们得到了具有变增长正则项的Rudin-Osher-Fatemi图像去噪问题变体的Euler-Lagrange方程。此外，我们提供了一个特征的l2梯度流的变增长总变化的抛物线PDE。

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引用次数: 0

On the boundedness of Fourier multipliers in terms of modulation spaces regularity 从调制空间正则性看傅里叶乘法器的有界性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.na.2025.113968

Ruhua Zhang , Guanggui Chen

In this paper, we establish the Hörmander type multiplier theorem for Fourier multipliers on Hardy spaces

H^{p} (R^{n})

for

0 < p \leq 1

, with regularity condition formulated in terms of modulation spaces

M_{s}^{r, q} (R^{n})

where

1 \leq r, q \leq \infty, s > \frac{n}{p} - \frac{n}{q}

. We further investigate the boundedness of Fourier multipliers on Lebesgue spaces

L^{p} (R^{n})

for

1 < p < \infty

through the interpolation. The conditions proposed in this paper not only improve those established by previous researchers but also refine the corresponding conclusions. Additionally, we introduce a novel multiplier theorem that incorporates the regularity condition formulated in terms of Wiener amalgam spaces

W_{s}^{r, q} (R^{n})

. Here the multiplier theorem may be of methodology to further studies of Fourier multipliers.

本文建立了Hardy空间HpRn上0<；p≤1的傅里叶乘子的Hörmander型乘子定理，正则性条件用1≤r，q≤∞,s>；np−nq的调制空间Msr，qRn表示。通过插值进一步研究了1<；p<；∞条件下Lebesgue空间LpRn上傅里叶乘子的有界性。本文提出的条件不仅完善了前人的条件，而且完善了前人的结论。此外，我们引入了一个新的乘法器定理，它包含了用维纳汞齐空间Wsr，qRn表述的正则性条件。在这里，乘数定理可能是进一步研究傅里叶乘数的方法论。

引用次数: 0

Morse index stability for Sacks–Uhlenbeck approximations for harmonic maps into a sphere 球面调和映射的Sacks-Uhlenbeck近似的Morse指数稳定性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-23 DOI: 10.1016/j.na.2025.113987

Francesca Da Lio, Tristan Rivière, Dominik Schlagenhauf

In this paper we consider sequences of

p

-harmonic maps,

p > 2

, from a closed Riemann surface

Σ

into the

n

-dimensional sphere

S^{n}

with uniform bounded energy. These are critical points of the energy

E_{p} (u) ≔ \int_{Σ} {(1 + {| \nabla u |}^{2})}^{p / 2} d v o l_{Σ} .

Our two main results are an improved pointwise estimate of the gradient in the neck regions around blow up points and the proof that the necks are asymptotically not contributing to the negativity of the second variation of the energy

E_{p} .

This allows us, in the spirit of the paper of the first and second authors in collaboration with Gianocca et al. (2022) , to show the upper semicontinuity of the Morse index plus nullity for sequences of

p

-harmonic maps into a sphere.

本文考虑了从封闭黎曼曲面Σ到具有均匀有界能量的n维球面Sn的p调和映射序列p>；2。这是能量的临界点Ep(u),∫Σ1+|∇u|2p/2dvolΣ。我们的两个主要结果是对爆炸点周围颈部区域梯度的改进的点向估计，以及颈部渐近地不影响能量Ep的第二次变化的负性的证明。这允许我们，本着第一和第二作者与Gianocca等人（2022）合作的论文精神，展示了球面上的p调和映射序列的莫尔斯指数加零的上半连续性。

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引用次数: 0

Evolution of convex closed curves under the generalized gradient flow of anisoperimetric ratio 广义等径比梯度流下凸闭合曲线的演化

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-21 DOI: 10.1016/j.na.2025.113980

Ze-Yu Ye, Xiao-Liu Wang

In this paper, we study a generalized gradient flow of anisoperimetric ratio, whose inner normal velocity contains a power of anisotropic curvature for convex closed curves. It is shown that for any embedded smooth closed convex initial curve, the flow exists globally and the curvature of evolving curves converges smoothly to the curvature of the boundary of the Wulff shape, which is determined by the given anisotropic function, as time goes to infinity.

本文研究了一类广义各向异性比梯度流，其内法向速度包含凸闭曲线各向异性曲率的幂次。结果表明，对于任意嵌入的光滑闭凸初始曲线，随着时间趋于无穷，流动是全局存在的，且演化曲线的曲率平滑地收敛于由给定各向异性函数决定的Wulff形状边界的曲率。

引用次数: 0

An inhomogeneous porous medium equation with non-integrable data: Asymptotics 具有不可积数据的非齐次多孔介质方程：渐近性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-15 DOI: 10.1016/j.na.2025.113979

Matteo Muratori , Troy Petitt , Fernando Quirós

We investigate the asymptotic behavior as

t \to + \infty

of solutions to a weighted porous medium equation in

R^{N}

, whose weight

ρ (x)

behaves at spatial infinity like

{| x |}^{- γ}

with subcritical power, namely

γ \in [0, 2)

. Inspired by some results (Alikakos and Rostamian, 1984; Kamin and Ughi, 1987) from the 1980s on the unweighted problem, we focus on solutions whose initial data

u_{0} (x)

are not globally integrable with respect to the weight and behave at infinity like

{| x |}^{- α}

, for

α \in (0, N - γ)

. In the special case

ρ (x) = {| x |}^{- γ}

and

u_{0} (x) = {| x |}^{- α}

we show that self-similar solutions of Barenblatt type, i.e. reminiscent of the usual source-type solutions, still exist, although they are no longer compactly supported. Moreover, they exhibit a transition phenomenon which is new even for the unweighted equation. We prove that such self-similar solutions are attractors for the original problem, and convergence takes place globally in suitable weighted

L^{p}

spaces for

p \in [1, \infty)

and even globally in

L^{\infty}

under some mild additional regularity assumptions on the weight. Among the fundamental tools that we exploit, it is worth mentioning a global smoothing effect for non-integrable data.

我们研究了RN中一个加权多孔介质方程解在t→+∞时的渐近行为，该方程的权值ρ(x)在空间无穷远处表现为具有次临界幂的|x|−γ，即γ∈[0,2]。受20世纪80年代关于无权问题的一些结果（Alikakos和Rostamian, 1984； Kamin和Ughi， 1987）的启发，我们重点研究了初始数据u0(x)对于权不是全局可积的解，并且对于α∈(0,N−γ)在无穷远处表现为|x|−α。在ρ(x)=|x|−γ和u0(x)=|x|−α的特殊情况下，我们证明了自相似的Barenblatt型解，即让人想起通常的源型解，仍然存在，尽管它们不再紧支持。此外，它们还表现出一种即使对未加权方程也是新的过渡现象。我们证明了这类自相似解是原问题的吸引子，并且在p∈[1，∞]的适当加权Lp空间中全局收敛，在一些对权的温和附加正则性假设下甚至在L∞上全局收敛。在我们利用的基本工具中，值得一提的是不可积数据的全局平滑效应。

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引用次数: 0

Travelling waves for Maxwell’s equations in nonlinear and symmetric media 非线性对称介质中麦克斯韦方程组的行波

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-15 DOI: 10.1016/j.na.2025.113976

Jarosław Mederski , Jacopo Schino

We look for travelling wave fields

E (x, y, z, t) = U (x, y) cos (k z + ω t) + \tilde{U} (x, y) sin (k z + ω t), (x, y, z) \in R^{3}, t \in R,

satisfying Maxwell’s equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy consisting of transverse magnetic field modes. In addition, we consider a general nonlinearity, controlled by an N-function.

我们寻找在非线性圆柱对称介质中满足麦克斯韦方程组的行波场E(x,y,z,t)=U(x,y)cos(kz+ωt)+U ~ (x,y)sin(kz+ωt),(x,y,z)∈R3,t∈R。我们得到了一系列由横向磁场模组成的发散能量的解。此外，我们考虑一个由n函数控制的一般非线性。

引用次数: 0

Traveling gravity-capillary waves with odd viscosity 行进重力-奇粘度毛细管波

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-11 DOI: 10.1016/j.na.2025.113975

Diego Alonso-Orán , Claudia García , Rafael Granero-Belinchón

In this note, we study the existence of traveling waves of a surface model in a non-newtonian fluid with odd viscosity. The proof relies on nonlinear bifurcation techniques.

本文研究了奇黏度非牛顿流体中表面模型行波的存在性。该证明依赖于非线性分岔技术。

引用次数: 0

Schottky invariant diffusion on the transcendent p-adic upper half plane 超越p进上半平面上的Schottky不变扩散

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-10 DOI: 10.1016/j.na.2025.113947

Patrick Erik Bradley

The transcendent part of the Drinfel’d

p

-adic upper half plane is shown to be a Polish space. Using Radon measures associated with regular differential 1-forms invariant under Schottky groups allows to construct self-adjoint diffusion operators as Laplacian integral operators with kernel functions determined by the

p

-adic absolute value on the complex

p

-adic numbers. Their spectra are explicitly calculated and the corresponding Cauchy problems for their associated heat equations are found to be uniquely solvable and to determine Markov processes having paths which are càdlàg. The heat kernels are shown to have explicitly given distribution functions, as well as boundary value problems associated with the heat equations under Dirichlet and von Neumann conditions are solved.

证明了德林菲尔p进上半平面的超越部分是一个波兰空间。利用与Schottky群下正则微分1-形式不变量相关的Radon测度，可以将自伴随扩散算子构造为拉普拉斯积分算子，其核函数由复p进数上的p进绝对值决定。明确地计算了它们的光谱，并发现其相关热方程的对应柯西问题是唯一可解的，并确定了路径为càdlàg的马尔可夫过程。结果表明，热核具有显式给定的分布函数，并解决了狄利克雷和冯·诺伊曼条件下与热方程相关的边值问题。

引用次数: 0

Resolvent estimates for the one-dimensional damped wave equation with unbounded damping 具有无界阻尼的一维阻尼波动方程的解析估计

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-10-10 DOI: 10.1016/j.na.2025.113978

Antonio Arnal

We study the generator

G

of the one-dimensional damped wave equation with unbounded damping at infinity. We show that the norm of the corresponding resolvent operator,

‖ {(G - λ)}^{- 1} ‖

, is approximately constant as

| λ | \to + \infty

on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane,

{\bar{ℂ}}_{-} ≔ {λ \in ℂ : Re λ \leq 0}

. Our proof rests on a precise asymptotic analysis of the norm of the inverse of

T (λ)

, the quadratic operator associated with

G

研究了无穷远处具有无界阻尼的一维阻尼波动方程的产生器G。证明了对应的解析算子‖(G−λ)−1‖在左手边复半平面的闭包中包含的有界宽度的垂直线上，其范数近似为|λ|→+∞。我们的证明依赖于T（λ）的逆模的精确渐近分析，即与G相关的二次算子。

引用次数: 0

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Nonlinear Analysis-Theory Methods & Applications

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