We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a BrunnMinkowski inequality and an Urysohn's type inequality for the Bernoulli Constant and we study the behavior of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior problem.
Concavity properties for elliptic free boundary problems / C. Bianchini; P. Salani. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 71:(2009), pp. 4461-4470. [10.1016/j.na.2009.03.004]
Concavity properties for elliptic free boundary problems
BIANCHINI, CHIARA;SALANI, PAOLO
2009
Abstract
We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a BrunnMinkowski inequality and an Urysohn's type inequality for the Bernoulli Constant and we study the behavior of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior problem.
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