Classification of global solutions of a free boundary problem in the plane
Serena Dipierro
University of Western Australia, Crawley, AustraliaAram L. Karakhanyan
The University of Edinburgh, UKEnrico Valdinoci
University of Western Australia, Crawley, Australia
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Abstract
We classify non-trivial, non-negative, positively homogeneous solutions of the 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 . The proof relies on several bespoke results for ordinary differential equations.
Cite this article
Serena Dipierro, Aram L. Karakhanyan, Enrico Valdinoci, Classification of global solutions of a free boundary problem in the plane. Interfaces Free Bound. 25 (2023), no. 3, pp. 455–490
DOI 10.4171/IFB/494