Data di Pubblicazione:
2008
Citazione:
Analysis and geometry on worms domains / S.G. Krantz, M.M. Peloso. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 18:2(2008), pp. 478-510. [10.1007/s12220-008-9021-3]
Abstract:
In this primarily expository article, we study the analysis of the Diederich-Fornæss worm domain in complex Euclidean space. We review its importance as a domain with nontrivial Nebenhülle, and as a counterexample to a number of basic questions in complex geometric analysis. Then we discuss its more recent significance in the theory of partial differential equations: the worm is the first smoothly bounded, pseudoconvex domain to exhibit global non-regularity for the D-Neumann problem. We take this opportunity to prove a few new facts. Next, we turn to specific properties of the Bergman kernel for the worm domain. An asymptotic expansion for this kernel is considered, and applications to function theory and analysis on the worm are provided.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Worm domain ; Bergman kernel ; Bergman projection ; Automorphism group ; D-Neumann problem
Elenco autori:
S.G. Krantz, M.M. Peloso
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