Geodesic
Convexity of level sets for solutions to nonlinear elliptic problems in convex rings
Electronic journal of differential equations, Tome 2006 (2006)
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__a141,
     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},
     year = {2006},
     volume = {2006},
     zbl = {1128.35320},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a141/}
}
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AU  - Salani,  Paolo
TI  - Convexity of level sets for solutions to nonlinear elliptic problems in convex rings
JO  - Electronic journal of differential equations
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VL  - 2006
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%A Salani,  Paolo
%T Convexity of level sets for solutions to nonlinear elliptic problems in convex rings
%J Electronic journal of differential equations
%D 2006
%V 2006
%U http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a141/
%G en
%F EJDE_2006__2006__a141
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__a141/