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arXiv · 2008.12734

On nonminimizing solutions of elliptic free boundary problems

Kanishka Perera
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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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Kanishka Perera. 2020-08-28. On nonminimizing solutions of elliptic free boundary problems. https://arxiv.org/abs/2008.12734

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