The Generalized Dirichlet Problem for the Monge - Ampère Equation in Polydisc

EasyChair Preprint 15787

Abstract

This article examines the Dirichlet problem for the Monge-Ampère equation in the polydisc. It demonstrates that a solution exists for the Dirichlet problem when the boundary function is extended in a plurisubharmonic manner to a small neighborhood of the boundary of the domain. Based on the results of Walsh and Sadullaev, the continuity of the solution and its construction method are established. This study holds significant importance for both theoretical mathematical problems and applications

Keyphrases: Maximal function, plurisubharmonic function, pseudoconvex domain, subharmonic function

@booklet{EasyChair:15787,
  author    = {Mokhira Vaisova},
  title     = {The Generalized Dirichlet Problem for the Monge - Ampère Equation in Polydisc},
  howpublished = {EasyChair Preprint 15787},
  year      = {EasyChair, 2025}}