Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations
arXiv:1309.4343 · doi:10.1007/s00526-015-0890-6
Abstract
We obtain an error estimate between viscosity solutions and δ-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is Lipschitz-continuous in space with linear growth in the Hessian. We also establish a rate of convergence for monotone and consistent finite difference approximation schemes for such equations.
37 pages; improved exposition from previous version