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Lectures on the ℒ2-Sobolev Theory of...

Straube, Emil J.,

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Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem/ Emil J. Straube
Author:	Straube, Emil J.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2010,
Description:	1 online resource (214 pages)
Subject:	Differential equations -
Online resource:	https://doi.org/10.4171/076
Online resource:	https://www.ems-ph.org/img/books/straube.jpg
ISBN:	9783037195765

Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem
Straube, Emil J.,

Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem[electronic resource] /Emil J. Straube - Zuerich, Switzerland :European Mathematical Society Publishing House,2010 - 1 online resource (214 pages) - ESI Lectures in Mathematics and Physics (ESI).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037195765

Standard No.: 10.4171/076doiSubjects--Topical Terms:

704075
Differential equations

Lectures on the ℒ2-Sobolev Theory of the ∂-Neumann problem
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