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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-25 DOI:10.1016/j.na.2024.113610

Matteo Rizzi , Panayotis Smyrnelis

引用次数: 0

Abstract

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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半线性椭圆 P.D.E. 解的一些刚性结果和渐近特性

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.