Global Regularity of the @-neumann Problem: a Survey of the L2-sobolev Theory
نویسنده
چکیده
The fundamental boundary value problem in the function theory of several complex variables is the ∂-Neumann problem. The L2 existence theory on bounded pseudoconvex domains and the C∞ regularity of solutions up to the boundary on smooth, bounded, strongly pseudoconvex domains were proved in the 1960s. On the other hand, it was discovered quite recently that global regularity up to the boundary fails in some smooth, bounded, weakly pseudoconvex domains. We survey the global regularity theory of the ∂-Neumann problem in the setting of L2 Sobolev spaces on bounded pseudoconvex domains, beginning with the classical results and continuing up to the frontiers of current research. We also briefly discuss the related global regularity theory of the Bergman projection.
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