Power convexity of a class of elliptic equations involving the Hessian operator in a 3-dimensional bounded convex domain

Abstract

In this paper, we are concerned with power convexity of a class of fully nonlinear elliptic equations involving the Hessian operator in a bounded and strictly convex domain in R3. We use the constant rank theorem and deformation technique to prove that some power of the smooth admissible solution is strictly convex. As a corollary, we deduce that all the level sets of the solution are strictly convex.