ENGLISH

Hodge Decomposition—A Method for Solving Boundary Value Problems

By Günter Schwarz (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1995
ISBN
978-3-540-60016-9, 978-3-540-49403-4
DOI
10.1007/BFb0095978
Language
english
Format
PDF
Filesize
2 MB (2034115 bytes)
Series
Lecture Notes in Mathematics 1607
Edition
1
Pages
164\160
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Potential Theory; Manifolds and Cell Complexes (in

Description

Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.

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