TY  - BOOK
AU  - Straube,Emil J.
AU  - Straube,Emil J.
TI  - Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem
T2  - ESI Lectures in Mathematics and Physics (ESI)
SN  - 9783037195765
PY  - 2010///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential equations
KW  - bicssc
KW  - Several complex variables and analytic spaces
KW  - msc
KW  - Partial differential equations
N1  - Restricted to subscribers
N2  - This book provides a thorough and self-contained introduction to the ∂-Neumann problem, leading up to current research, in the context of the ℒ2-Sobolev theory on bounded pseudoconvex domains in ℂn. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrödinger International Institute for Mathematical Physics and at Texas A&M University.  The introductory chapter  provides an overview of the contents and puts them in historical perspective. The second chapter  presents the basic ℒ2-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research.  Prerequisites are a solid background in basic complex and functional analysis, including the elementary ℒ2-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch
UR  - https://doi.org/10.4171/076
UR  - http://www.ems-ph.org/img/books/straube.jpg
ER  -