On the convexity of some free boundaries
Summary: 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.
scientific article; zbMATH DE number 5665699