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Hodge Decomposition - A Method for Solving Boundary Value Problems

  • Book
  • © 1995

Overview

Authors:
  1. Günter Schwarz
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1607)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • Günter Schwarz
    Pages 1-8

  3. Analysis of differential forms

    • Günter Schwarz
    Pages 9-58

  4. The hodge decomposition

    • Günter Schwarz
    Pages 59-112

  5. Boundary value problems for differential forms

    • Günter Schwarz
    Pages 113-145

  6. Back Matter

    Pages 147-155
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Hodge Decomposition - A Method for Solving Boundary Value Problems

  • Authors: Günter Schwarz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095978

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-60016-9Published: 14 July 1995

  • eBook ISBN: 978-3-540-49403-4Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 164

  • Topics: Potential Theory, Manifolds and Cell Complexes (incl. Diff.Topology)

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