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Convexity estimates for nonlinear elliptic equations and application to free boundary problems

✍ Scribed by Jean Dolbeault; Régis Monneau

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
187 KB
Volume
19
Category
Article
ISSN
0294-1449

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✦ Synopsis

We prove the convexity of the set which is delimited by the free boundary corresponding to a quasi-linear elliptic equation in a 2-dimensional convex domain. The method relies on the study of the curvature of the level lines at the points which realize the maximum of the normal derivative at a given level, for analytic solutions of fully nonlinear elliptic equations. The method also provides an estimate of the gradient in terms of the minimum of the (signed) curvature of the boundary of the domain, which is not necessarily assumed to be convex.  2002 Éditions scientifiques et médicales Elsevier SAS

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