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

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

2009-10-25

arxiv.org/abs/0910.4721v1

Journal of Differential Equations 225, 1 (2006) 202 -- 241

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.jde.2005.09.004

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.

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