On the convexity of some free boundaries | Zendy

Antonio Greco | Zendy; Bernd Kawohl | Zendy

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On the convexity of some free boundaries

Author(s) -

Antonio Greco,

Bernd Kawohl

Publication year - 2009

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/220

Subject(s) - convexity , quasiconvex function , bernoulli's principle , boundary (topology) , mathematics , free boundary problem , boundary value problem , mathematical analysis , mathematical optimization , regular polygon , geometry , convex analysis , convex optimization , physics , economics , financial economics , thermodynamics

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\udboundaries. As examples we present the so-called dam problem, a free boundary problem modelling\udpollution and a Bernoulli problem. Moreover, we prove strict convexity of the wet region in the dam\udproblem in arbitrary dimensions.\u

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