Local $C^{0,\alpha }$ Estimates for Viscosity Solutions of Neumann-type Boundary Value Problems

Abstract

In this article, we prove the local $C^{0,\alpha }$ regularity and provide $C^{0,\alpha }$ estimates for viscosity solutions of fully nonlinear, possibly degenerate, elliptic equations associated to linear or nonlinear Neumann type boundary conditions. The interest of these results comes from the fact that they are indeed regularity results (and not only a priori estimates), from the generality of the equations and boundary conditions we are able to handle and the possible degeneracy of the equations we are able to take in account in the case of linear boundary conditions.

Cited by in corpus (5)

• Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations
• Homogenization for nonlinear PDEs in general domains with oscillatory Neumann boundary data
• Homogenization of oblique boundary value problems
• On the Large Time Behavior of Solutions of the Dirichlet problem for Subquadratic Viscous Hamilton-Jacobi Equations
• Principal eigenvalues for Isaacs operators with Neumann boundary conditions