English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present a viscosity approach to the Dirichlet problem for the complex Monge–Ampère equation $${\det u_{\bar{j} k} = f (x, u)}$$ . Our approach differs from previous viscosity approaches to this equation in several ways: it is based on contact set techniques (the Alexandrov–Bakelman–Pucci estimate), on extensive applications of sup-inf convolutions, and on a relation between real and complex Hessians. More specifically, this paper includes a notion of viscosity solutions; a comparison principle and a solvability theorem; the equivalence between viscosity and pluripotential solutions; an estimate of the modulus of continuity of a solution in terms of that of a given subsolution and of the right-hand side f; and an Alexandrov–Bakelman–Pucci type of L∞-estimate.

A viscosity approach to the Dirichlet problem for complex Monge–Ampère equations