Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problem

Emil J. Straube

Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problem

Complex Variables 2007-05-23 v1 Analysis of PDEs

Authors: Emil J. Straube

Abstract

The $\bar{\partial}$ -Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not all, pseudoconvex domains. We discuss several recent developments in the $L^{2}$ -Sobolev theory of the $\bar{\partial}$ -Neumann problem that concern compactness and global regularity.

Keywords

$\bar{\partial}$-Neumann problem $L^{2}$-Sobolev theory several complex variables pseudoconvex domains global regularity compactness

Cite

@article{arxiv.math/0601128,
  title  = {Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problem},
  author = {Emil J. Straube},
  journal= {arXiv preprint arXiv:math/0601128},
  year   = {2007}
}

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