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.
1
Università degli Studi di Cagliari, Italy
2
Universität Köln, Germany
Antonio Greco; Bernd Kawohl. On the convexity of some free boundaries. Interfaces and free boundaries, Tome 11 (2009) no. 4, pp. 503-514. doi: 10.4171/ifb/220
@article{10_4171_ifb_220,
author = {Antonio Greco and Bernd Kawohl},
title = {On the convexity of some free boundaries},
journal = {Interfaces and free boundaries},
pages = {503--514},
year = {2009},
volume = {11},
number = {4},
doi = {10.4171/ifb/220},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/220/}
}
TY - JOUR
AU - Antonio Greco
AU - Bernd Kawohl
TI - On the convexity of some free boundaries
JO - Interfaces and free boundaries
PY - 2009
SP - 503
EP - 514
VL - 11
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UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/220/
DO - 10.4171/ifb/220
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