Seminario Dottorato: The d-bar-Neumann problem

Wednesday 14 October 2009 - Tran Vu Khanh

ARGOMENTI: Seminari Dottorato

Wednesday 14 October 2009 h. 15:00, room 2AB/60
Tran Vu Khanh (Univ. Padova, Dip. Mat.)
"The d-bar-Neumann problem"

The d-bar-Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann system. The main tool to prove regularity of solutions in the study of this problem are L2-estimates: subelliptic estimates, superlogarithmic estimates, compactness estimates.
In the first part of the talk we give motivation and classical results on this problem. In the second part, we introduce general estimates for "gain of regularity" of solutions of this problem and relate it to the existence of weights with large Levi-form at the boundary.
(Keywords: q-pseudoconvex/concave domains, subelliptic estimates, superlogarithmic estimates, compactness estimates, finite type, infinite type. MSC: 32D10, 32U05, 32V25.)

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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