The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations

  • Authors
  • Jan Chabrowski

Part of the Lecture Notes in Mathematics book series (LNM, volume 1482)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Jan Chabrowski
    Pages 1-4
  3. Jan Chabrowski
    Pages 7-19
  4. Jan Chabrowski
    Pages 20-45
  5. Jan Chabrowski
    Pages 46-66
  6. Jan Chabrowski
    Pages 67-77
  7. Jan Chabrowski
    Pages 78-89
  8. Jan Chabrowski
    Pages 90-103
  9. Jan Chabrowski
    Pages 104-116
  10. Jan Chabrowski
    Pages 117-130
  11. Jan Chabrowski
    Pages 131-141
  12. Back Matter
    Pages 168-173

About this book

Introduction

The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.

Keywords

Dirichlet problem Elliptic equations Potential theory Sobolev space harmonic analysis partial differential equation weighted Sobolev spaces

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095750
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54486-9
  • Online ISBN 978-3-540-38400-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book