On nonminimizing solutions of elliptic free boundary problems

DOI10.1007/S00526-024-02739-ZarXiv2008.12734OpenAlexW4396699741MaRDI QIDQ6347932

Kanishka Perera

Publication date: 28 August 2020

Abstract: We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and subcritical superlinear free boundary problems, and establish full regularity of the free boundary in dimension $N=2$ and partial regularity in higher dimensions.

Full work available at URL: https://doi.org/10.1007/s00526-024-02739-z

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)

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