Game-theoretic approach to Hölder regularity for PDEs involving eigenvalues of the Hessian

Abstract

We prove a local Hölder estimate with an exponent 0 < δ < 1 2 for solutions of the dynamic programming principleThe proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDEu) are the eigenvalues of the Hessian.