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

Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci

Research output: Working paperPreprint

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 Published - 22 Mar 2022

• math.AP

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