JournalsifbVol. 25, No. 3pp. 455–490

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

  • Serena Dipierro

    University of Western Australia, Crawley, Australia

  • Aram L. Karakhanyan

    The University of Edinburgh, UK

  • Enrico Valdinoci

    University of Western Australia, Crawley, Australia
Classification of global solutions of a free boundary problem in the plane cover
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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