半线性椭圆 P.D.E. 解的一些刚性结果和渐近特性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-07-25 DOI:10.1016/j.na.2024.113610

Matteo Rizzi , Panayotis Smyrnelis

引用次数: 0

摘要

我们将介绍一些半线性椭圆方程解的刚性结果，这些方程的形式为，其中是一个具有局部最小值和局部最大值的相当普遍的势。我们对 Liouville 型定理和对称性结果特别感兴趣，它们概括了有关 Cahn-Hilliard 方程的一些已知事实。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some rigidity results and asymptotic properties for solutions to semilinear elliptic P.D.E.

We will present some rigidity results for solutions to semilinear elliptic equations of the form $Δ u = W^{'} (u)$ , where $W$ is a quite general potential with a local minimum and a local maximum. We are particularly interested in Liouville-type theorems and symmetry results, which generalise some known facts about the Cahn–Hilliard equation.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.