Resumen de Aspects of the L2-Sobolev theory of the �Ý-Neumann

Emil J. Straube

• The �Ý-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 theL2-Sobolev theory of the �Ý-Neumann problem that concern compactness and global regularity.