Classification of global solutions of a free boundary problem in the plane
Analysis of PDEs
2022-09-08 v2
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 . The proof relies on several bespoke results for ordinary differential equations.
Keywords
Cite
@article{arxiv.2203.11663,
title = {Classification of global solutions of a free boundary problem in the plane},
author = {Serena Dipierro and Aram Karakhanyan and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2203.11663},
year = {2022}
}