Geodesic
Convexity of level sets for solutions to nonlinear elliptic problems in convex rings
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\Omega=\Omega_0\setminus\overline\Omega_1$.
Classification : 35J25, 35J65
Keywords: elliptic equations, convexity of level sets, quasi-concave envelope 
@article{EJDE_2006__2006__a41,
     author = {Cuoghi, Paola and Salani, Paolo},
     title = {Convexity of level sets for solutions to nonlinear elliptic problems in convex rings},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a41/}
}
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Cuoghi, Paola; Salani, Paolo. Convexity of level sets for solutions to nonlinear elliptic problems in convex rings. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a41/