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

2022/03/22 by Dipierro, Serena, Karakhanyan, Aram, Valdinoci, Enrico · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.11663

Abstract

We classify nontrivial, nonnegative, positively homogeneous solutions of the equation Δu=γu^γ-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 γ. The proof relies on several bespoke results for ordinary differential equations.

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• On the existence of solutions to some singular parabolic free boundary problems
• Regularity and classification of the free boundary for a Monge-Ampère obstacle problem

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