Aspects of the L²-Sobolev theory of the ∂-Neumann problem

الأصل · EN

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 L²-Sobolev theory of the ∂-Neumann problem that concern compactness and global regularity.