A Viscosity Approach to the Dirichlet Problem for Complex Monge-Amp\`ere Equations
Complex Variables
2010-11-23 v2 Analysis of PDEs
Abstract
The Dirichlet problem for complex Monge-Amp\'ere equations with continuous data is considered. In particular, a notion of viscosity solutions is introduced; a comparison principle and a solvability theorem are proved; the equivalence between viscosity and pluripotential solutions is established; and an ABP-type of -estimate is achieved.
Cite
@article{arxiv.1010.1292,
title = {A Viscosity Approach to the Dirichlet Problem for Complex Monge-Amp\`ere Equations},
author = {Yu Wang},
journal= {arXiv preprint arXiv:1010.1292},
year = {2010}
}
Comments
This version contains a new proof of existence of solution, in which semi-continuous functions are avoided. It also gives an estimate of modulus of continuity of solution in terms of datum and subsolution. An corollary of ABP estimate is added. A few changes on presentation have been included