Concavity properties for free boundary elliptic problems
Analysis of PDEs
2010-01-07 v2
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.
Cite
@article{arxiv.0810.4842,
title = {Concavity properties for free boundary elliptic problems},
author = {C. Bianchini and P. Salani},
journal= {arXiv preprint arXiv:0810.4842},
year = {2010}
}
Comments
12 pages. This is a revised version of the already published paper, which includes the corrections contained in the Corrigendum available online at http://dx.doi.org/10.1016/j.na.2009.11.031