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.
Power concavity for solutions of nonlinear elliptic problems in convex domains / M. Bianchini; P. Salani. - STAMPA. - (2013), pp. 35-48. [10.1007/978-88-470-2841-8_3]
Power concavity for solutions of nonlinear elliptic problems in convex domains
BIANCHINI, MASSIMILIANO;SALANI, PAOLO
2013
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.
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