平面上自由边界问题整体解的分类

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries 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

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.