Weak Harnack inequalities for eigenvalues and constant rank theorems

Abstract

We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian-Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

15 pages

References in corpus (1)

• Strong space-time convexity and the heat equation

Cited by in corpus (1)

• Constant rank theorems for curvature problems via a viscosity approach