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arXiv · 2203.11663

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

Serena Dipierro·Aram Karakhanyan·Enrico Valdinoci
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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.

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Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci. 2022-03-22. Classification of global solutions of a free boundary problem in the plane. https://arxiv.org/abs/2203.11663

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