ESI Senior Research Fellow Program, spring term 2005
The L2-Sobolev theory of the d-bar-Neumann problem
Course of advanced graduate lectures by
Professor Emil Straube
(Texas A&M University)
lectures: May 18, 20, 24, 25 and June 1, 3 at 13:00 - 15:00 (to be continued in fall term)
This course treats the L2-Sobolev regularity theory of the
d-bar-Neumann problem on bounded pseudoconvex domains in complex
Euclidean space, with an emphasis on global regularity (in
L2-Sobolev spaces) and compactness. Starting with some classical
results from the sixties which form the bedrock of the theory, the
course will lead to current developments in the area.
A brief outline is as follows: the L2 existence theory, strongly pseudoconvex
domains, regularity in general pseudoconvex domains, finite type and
subelliptic estimates, compactness, global regularity. Except for the
chapter on finite type and subelliptic estimates, I plan to give
complete proofs of the main results. The course will be at the
advanced graduate level; in particular, a solid background in real,
functional, and complex analysis (including basic several complex
variables) is expected.
ESI Senior Research Fellow Program coordinated by Prof. Joachim
Schwermer, Fakultät für Mathematik, Universität Wien,
Nordbergstraße 15, A-1090 Wien (Joachim.Schwermer@univie.ac.at).