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

Serena Dipierro; Aram Karakhanyan; Enrico Valdinoci

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

Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci

School of Mathematics

Research output: Working paper › Preprint

Abstract

We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} 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.

Original language	English
Publication status	Published - 22 Mar 2022

Keywords

math.AP

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2203.11663v1Submitted manuscript, 548 KB

https://arxiv.org/abs/2203.11663

Cite this

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KW - math.AP

M3 - Preprint

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

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

Abstract

Keywords

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Cite this