article

Title: A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations

Authors: Baojun Bian, Pengfei Guan, Xinan Ma and Lu Xu

Issue: Volume 60 (2011), Issue 1, 101-120

Abstract:

$We prove a constant rank theorem for the second fundamental form of the convex level surfaces of solutions to equations $F(D^2u,Du,u,x) = 0$ under a structural condition introduced by Bianchini-Longinetti-Salani in [C. Bianchini, M. Longinetti and P. Salani, \textit{Quasiconcave solutions to elliptic problems in convex rings}, Indiana Univ. Math. J. \textbf{58} (2009), 1565--1590].$