Aspects of the L2-Sobolev theory of the ∂̄-Neumann problem
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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. © 2006 European Mathematical Society.
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