Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations

Details Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations

2010-04-07

arxiv.org/abs/1004.1187v2

Mathematics

Analysis of PDEs

Scientific paper

We establish a geometric lower bound for the principal curvature of the level
surfaces of solutions to $F(D^2u, Du, u, x)=0$ in convex ring domains, under a
refined structural condition introduced by Bianchini-Longinetti-Salani in
\cite{BLS}. We also prove a constant rank theorem for the second fundamental
form of the convex level surfaces of these solutions.

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