Dirichlet Problem in Domains of ℂn

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2038)

Abstract

This lecture treats the Dirichlet problem for the homogeneous complex Monge–Ampère equation in domains Ω C n. The most important result, due to Bedford and Taylor [BT76], yields the optimal interior regularity of the solution when Ω = B is the unit ball. We provide a complete proof, following the simplifications of Demailly [Dem93].

Keywords

Maximum Principle Unit Ball Unit Disk Dirichlet Problem Pseudoconvex Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance

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