Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534

Abstract : 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.

CONVEXITY ESTIMATES FOR NONLINEAR ELLIPTIC EQUATIONS AND APPLICATION TO FREE BOUNDARY PROBLEMS

DOLBEAULT Jean, MONNEAU Regis

2000-32

07-09-2000

http://www.ceremade.dauphine.fr/preprint/CMD/2000-32.ps

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