Concavity properties for free boundary elliptic problems

C. Bianchini; P. Salani

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arXiv · 0810.4842

Concavity properties for free boundary elliptic problems

C. Bianchini·P. Salani

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Abstract

We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn's type inequality for the Bernoulli Constant and we study the behaviour of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior non-linear Bernoulli problem.

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C. Bianchini, P. Salani. 2010-01-07. Concavity properties for free boundary elliptic problems. https://arxiv.org/abs/0810.4842

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