BooksStandalone TitlesCollected Volumepp. 1453–1478

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

Emil J. Straube
Texas A&M University, College Station, United States

Aspects of the L^2-Sobolev theory of the <span style="text-decoration: overline;">∂</span>-Neumann problem cover

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Abstract

The ∂-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 ∂-Neumann problem that concern compactness and global regularity.