Concavity properties for free boundary elliptic problems

Mathematics – Analysis of PDEs

Scientific paper

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12 pages. This is a revised version of the already published paper, which includes the corrections contained in the Corrigendu

Scientific paper

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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