Pointwise boundary estimates for fully nonlinear elliptic equations with nonzero Dirichlet boundary conditions

Abstract

In this paper, we investigate boundary estimates for the Dirichlet problem for a class of fully nonlinear elliptic equations with general boundary conditions, including nonzero boundary conditions. Given specific structural conditions on the problem, we develop pointwise boundary upper and lower bound estimates for convex solutions based on the subsolution and supersolution method. The global H\"older regularity can be derived as a direct consequence of these pointwise boundary estimates. These results fundamentally hinge on careful descriptions of the convexity properties of both the domains and the functions involved. Moreover, previous results on Monge-Amp\`ere equations with nonzero Dirichlet boundary conditions can be regarded as a special case of our results.