Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 124, pp. 1-12.
Title: Convexity of level sets for solutions to nonlinear elliptic
problems in convex rings
Authors: Paola Cuoghi (Univ. degli Studi di Modena, Italy)
Paolo Salani (Univ. Dini, Firenze, Italy)
Abstract:
We find suitable assumptions for the quasi-concave
envelope $u^*$ of a solution (or a subsolution) $u$ of an elliptic
equation $F(x,u,\nabla u,D^2u)=0$ (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 a convex ring
$\Omega=\Omega_0\setminus\overline\Omega_1$.
Submitted June 23, 2005. Published October 11, 2006.
Math Subject Classifications: 35J25, 35J65.
Key Words: Elliptic equations; convexity of level sets;
quasi-concave envelope.