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On nonminimizing solutions of elliptic free boundary problems

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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.

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  1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA

    Kanishka Perera

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  1. Kanishka Perera
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Correspondence to Kanishka Perera.

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Communicated by P. H. Rabinowitz.

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Perera, K. On nonminimizing solutions of elliptic free boundary problems. Calc. Var. 63, 130 (2024). https://doi.org/10.1007/s00526-024-02739-z

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