A Viscosity Approach to the Dirichlet Problem for Complex Monge-Ampère Equations

Details A Viscosity Approach to the Dirichlet Problem for Complex Monge-Ampère Equations A Viscosity Approach to the Dirichlet Problem for Complex Monge-Ampère Equations

2010-10-06

arxiv.org/abs/1010.1292v2

Mathematics

Complex Variables

This version contains a new proof of existence of solution, in which semi-continuous functions are avoided. It also gives an e

Scientific paper

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 $L^{\infty}$-estimate is achieved.

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