Hodge Decomposition—A Method for Solving Boundary Value Problems

  • Authors
  • Günter Schwarz

Part of the Lecture Notes in Mathematics book series (LNM, volume 1607)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Günter Schwarz
    Pages 1-8
  3. Günter Schwarz
    Pages 9-58
  4. Günter Schwarz
    Pages 59-112
  5. Günter Schwarz
    Pages 113-145
  6. Back Matter
    Pages 147-155

About this book

Introduction

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.

Keywords

Boundary value problem Hodge theory Vector field differential equation manifold partial differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095978
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60016-9
  • Online ISBN 978-3-540-49403-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book