On the convexity of some free boundaries
نویسندگان
چکیده
We demonstrate that a method of Colesanti and Salani, which compares solutions of elliptic differential equations to their quasiconcave envelopes, can be extended to derive convexity of free boundaries. As examples we present the so-called dam problem, a free boundary problem modelling pollution and a Bernoulli problem. Moreover we prove strict convexity of the wet region in the dam problem in arbitrary dimensions.
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