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THE BREMERMANN-DIRICHLET PROBLEM FOR UNBOUNDED DOMAINS OF Cn
 

Summary: THE BREMERMANN-DIRICHLET PROBLEM FOR
UNBOUNDED DOMAINS OF Cn
ALEXANDRU SIMIONIUC, GIUSEPPE TOMASSINI
ABSTRACT. Given an unbounded strongly pseudoconvex domain and
a continuous real valued function h defined on b, we study the ex-
istence of a (maximal) plurisubharmonic function on such that
|b = h.
CONTENTS
1. Introduction 1
2. Preliminaries 3
2.1. The Perron-Bremermann function 3
2.2. The Bremermann-Dirichlet problem 5
3. Existence of continuous solutions for unbounded domains 6
4. Maximal solutions for unbounded strongly convex domains 8
4.1. Existence 8
4.2. Continuity 14
4.3. Some examples 17
5. The case of unbounded strongly pseudoconvex domains 19
6. Existence of a pluriharmonic solution 21
7. A generalization for q-plurisubharmonic functions 22

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics