平面上自由边界问题整体解的分类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-13 DOI:10.4171/ifb/494

Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci

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引用次数: 2

摘要

我们对平面上方程$$ \Delta u=\gamma u^{\gamma-1} $$的非平凡、非负、正齐次解进行分类。问题的动机是分析经典的Alt-Phillips自由边界问题，但这里考虑负指数$\gamma$。这个证明依赖于对常微分方程的几个预定结果。

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Classification of global solutions of a free boundary problem in the plane

We classify non-trivial, non-negative, positively homogeneous solutions of the equation $$ \Delta u=\gamma u^{\gamma-1} $$ in the plane. The problem is motivated by the analysis of the classical Alt–Phillips free boundary problem, but considered here with negative exponents $\gamma$. The proof relies on several bespoke results for ordinary differential equations.

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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.