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

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

2006-01-06

arxiv.org/abs/math/0601128v1

Mathematics

Complex Variables

Scientific paper

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.

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