BooksStandalone TitlesCollected Volumepp. 1453–1478

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

  • Emil J. Straube

    Texas A&M University, College Station, United States
Aspects of the <em>L</em><sup>2</sup>-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.