Power concavity for solutions of nonlinear elliptic problems in convex domains

Abstract

We investigate convexity properties of solutions to elliptic Dirichlet problems in convex domains. In particular we give conditions on the operator F such that a suitable power of a positive solution u of a fully nonlinear equation F(x,u,Du,D2u)=0 in a convex domain Ω, vanishing on ∂Ω, is concave.