We find suitable assumptions for the quasi-concave envelope of a solution (or a subsolution) u of an elliptic equation F(x, u,ru,D2u) = 0 (possibly fully nonlinear) to be a viscosity subsolution of the same equation. We apply this result to study the convexity of level sets of solutions to elliptic Dirichlet problems in convex rings.
Convexity of level sets for solutions to non-linear elliptic problems in convex rings / P. CUOGHI; P. SALANI. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - ELETTRONICO. - 2006:(2006), pp. 1-12.
Convexity of level sets for solutions to non-linear elliptic problems in convex rings
SALANI, PAOLO
2006
Abstract
We find suitable assumptions for the quasi-concave envelope of a solution (or a subsolution) u of an elliptic equation F(x, u,ru,D2u) = 0 (possibly fully nonlinear) to be a viscosity subsolution of the same equation. We apply this result to study the convexity of level sets of solutions to elliptic Dirichlet problems in convex rings.
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