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arXiv · 1009.1277

A Bernoulli problem with non constant gradient boundary constraint

Chiara Bianchini
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Abstract

We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex.

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Chiara Bianchini. 2010-09-07. A Bernoulli problem with non constant gradient boundary constraint. https://arxiv.org/abs/1009.1277

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