Nonlinear Analysis-Theory Methods & Applications最新文献

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A geometrical approach to the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces sobolev - slobodecki空间中尖锐Hardy不等式的几何逼近

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-09-25 DOI: 10.1016/j.na.2025.113948

Francesca Bianchi , Giorgio Stefani , Anna Chiara Zagati

We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical flavor and equivalently reformulates the sharp constant in the limit case

p = 1

as the Cheeger constant for the fractional perimeter and the Lebesgue measure with a suitable weight. As a by-product, we obtain new lower bounds on the sharp constant in the 1-dimensional case, even for non-convex sets, some of which optimal in the case

p = 1

本文对Brasco等人关于凸集上分数阶Hardy不等式尖锐常数的问题给出了部分否定的回答。我们的方法具有几何风味，并等效地将极限情况下p=1的锐常数重新表述为分数周长的Cheeger常数和具有适当权重的勒贝格测度。作为一个副产品，我们得到了一维情况下尖锐常数的新下界，即使对于非凸集也是如此，其中一些在p=1的情况下是最优的。

引用次数: 0

Existence of multiple solutions for the generalized abelian Chern–Simons–Higgs model on a torus 环面上广义阿贝尔chen - simons - higgs模型的多重解的存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-09-25 DOI: 10.1016/j.na.2025.113950

Jongmin Han, Kyungwoo Song

We construct multiple solutions of the generalized self-dual abelian Chern–Simons–Higgs equation in a two-dimensional flat torus by the topological degree method.

利用拓扑度方法构造了二维平面环面上广义自对偶阿贝耳chen - simons - higgs方程的多个解。

引用次数: 0

Particle approximation of nonlocal interaction energies 非局部相互作用能量的粒子近似

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-10-07 DOI: 10.1016/j.na.2025.113974

Davide Carazzato , Aldo Pratelli , Ihsan Topaloglu

We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies

Γ

-converge in the weak-

*

topology to the Riesz functional defined over the space of probability measures. We also address the minimization problem for the discretized energies, and prove the existence of minimal configurations of particles in a very general and natural setting.

我们考虑具有一般相互作用核的riesz型非局部能量及其与粒子系统相关的离散化。我们证明了弱- *拓扑中的离散能量Γ-converge在概率测度空间上定义的Riesz泛函。我们还讨论了离散能量的最小化问题，并证明了在非常一般和自然的情况下粒子的最小构型的存在性。

引用次数: 0

Geodesic loops and orthogonal geodesic chords without self-intersections 无自交的测地线环和正交测地线弦

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-09-26 DOI: 10.1016/j.na.2025.113952

Hans-Bert Rademacher

We show that for a generic Riemannian metric on a compact manifold of dimension

n \geq 3

all geodesic loops based at a fixed point have no self-intersections. We also show that for an open and dense subset of the space of Riemannian metrics on an

n

-disc with

n \geq 3

and with a strictly convex boundary there are

n

geometrically distinct orthogonal geodesic chords without self-intersections. We use a perturbation result for intersecting geodesic segments of the author Rademacher (2024) and a genericity statement due to Bettiol and Giambò (2010) and existence results for orthogonal geodesic chords by Giambò et al. (2018).

我们证明了在维数n≥3的紧化流形上的一般黎曼度量，所有基于不动点的测地线环都没有自交。我们还证明了对于n≥3且边界为严格凸的n-圆盘上的黎曼度量空间的开密子集，存在n条几何上不同的无自交的正交测地线弦。我们使用了作者Rademacher（2024）的相交测地线段的摄动结果、Bettiol和Giambò（2010）的一般性陈述以及Giambò等人（2018）的正交测地线弦的存在性结果。

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 : 2026-02-01 Epub 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

The Dirichlet problem on lower dimensional boundaries: Schauder estimates via perforated domains 低维边界上的Dirichlet问题：通过穿孔区域的Schauder估计

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-10-07 DOI: 10.1016/j.na.2025.113973

Gabriele Fioravanti

In this paper, we investigate the Dirichlet problem on lower dimensional manifolds for a class of weighted elliptic equations with coefficients that are singular on such sets. Specifically, we study the problem

(\begin{matrix} - div ({| y |}^{a} A (x, y) \nabla u) = {| y |}^{a} f + div ({| y |}^{a} F), \\ u = ψ, on Σ_{0}, \end{matrix})

where

(x, y) \in R^{d - n} \times R^{n}

2 \leq n \leq d

a + n \in (0, 2)

, and

Σ_{0} = {| y | = 0}

is the lower dimensional manifold where the equation loses uniform ellipticity.

Our primary objective is to establish

C^{0, α}

and

C^{1, α}

regularity estimates up to

Σ_{0}

, under suitable assumptions on the coefficients and the data. Our approach combines perforated domain approximations, Liouville-type theorems and a blow-up argument.

本文研究了一类系数为奇异的加权椭圆型方程在低维流形上的Dirichlet问题。具体来说，我们研究了−div(|y|aA(x,y)∇u)=|y|af+div(|y| af),u=ψ,onΣ0，其中(x,y)∈Rd - n×Rn, 2≤n≤d, a+n∈(0,2)，Σ0={|y|=0}是方程失去一致椭圆性的低维流形。我们的主要目标是在对系数和数据的适当假设下，建立到Σ0的C0，α和C1，α正则性估计。我们的方法结合了穿孔域近似、liouville型定理和一个放大论证。

引用次数: 0

A Mean Field Game system and a related deterministic optimal control problem 平均场博弈系统及相关的确定性最优控制问题

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-10-07 DOI: 10.1016/j.na.2025.113977

Ştefana-Lucia Aniţa

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler–Lagrange system for an optimal control problem related to a Fokker–Planck equation with control in the drift. One derives the existence of a weak solution to the MFG system and under more restrictive assumptions one proves some uniqueness results.

本文研究了与大种群动态博弈纳什均衡相关的平均场博弈（MFG）系统。一个证明了MFG系统可以被看作是一个最优控制问题的欧拉-拉格朗日系统，该最优控制问题与漂移中的控制Fokker-Planck方程有关。导出了MFG系统弱解的存在性，并在更严格的假设条件下证明了一些唯一性结果。

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 : 2026-02-01 Epub 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

Γ-convergence of higher-order phase transition models Γ-convergence的高阶相变模型

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-10-09 DOI: 10.1016/j.na.2025.113971

Denis Brazke , Gianna Götzmann , Hans Knüpfer

We investigate the asymptotic behavior as

ɛ \to 0

of singularly perturbed phase transition models of order

n \geq 2

, given by

G_{ɛ}^{λ, n} [u] ≔ \int_{I} \frac{1}{ɛ} W (u) - λ ɛ^{2 n - 3} {(u^{(n - 1)})}^{2} + ɛ^{2 n - 1} {(u^{(n)})}^{2} d x, u \in W^{n, 2} (I),

where

λ > 0

is fixed,

I \subset R

is an open bounded interval, and

W \in C^{0} (R)

is a suitable double-well potential. We find that there exists a positive critical parameter depending on

W

and

n

, such that the

Γ

-limit of

G_{ɛ}^{λ, n}

with respect to the

L^{1}

-topology is given by a sharp interface functional in the subcritical regime. The cornerstone for the corresponding compactness property is a novel nonlinear interpolation inequality involving higher-order derivatives, which is based on Gagliardo–Nirenberg type inequalities.

研究了n≥2阶奇异摄动相变模型的渐近性，其中λ λ，n[u]是∫I1 ^ W(u)−λ ^ 2n−3(u(n−1))2+ ^ 2n−1(u(n))2dx,u∈Wn,2(I)，其中λ ^ gt；0是固定的，I∧R是一个开有界区间，W∈C0(R)是一个合适的双阱势。我们发现存在一个依赖于W和n的正临界参数，使得G λ，n关于l1拓扑的Γ-limit由亚临界区中的锐界面泛函给出。该紧性的基础是基于Gagliardo-Nirenberg型不等式的一种涉及高阶导数的非线性插值不等式。

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 : 2026-02-01 Epub 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

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