Skip to main content
SpringerLink
Log in

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

  • Book
  • © 1991

Overview

Authors:
  1. Jan Chabrowski
    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (11 chapters)

  1. Front Matter

    Pages I-VI
    Download chapter PDF

  2. Introduction

    • Jan Chabrowski
    Pages 1-4

  3. Weighted Sobolev space \(\tilde W^{1,2}\)

    • Jan Chabrowski
    Pages 7-19

  4. The Dirichlet problem in a half-space

    • Jan Chabrowski
    Pages 20-45

  5. The Dirichlet problem in a bounded domain

    • Jan Chabrowski
    Pages 46-66

  6. Estimates of derivatives

    • Jan Chabrowski
    Pages 67-77

  7. Harmonic measure

    • Jan Chabrowski
    Pages 78-89

  8. Exceptional sets on the boundary

    • Jan Chabrowski
    Pages 90-103

  9. Applications of the L 2-method

    • Jan Chabrowski
    Pages 104-116

  10. Domains with C1,α-boundary

    • Jan Chabrowski
    Pages 117-130

  11. The space C n−1(\(\bar Q\))

    • Jan Chabrowski
    Pages 131-141

  12. Cn−1-estimate of the solution of the Dirichlet problem with L2-boundary data

    • Jan Chabrowski
    Pages 142-167

  13. Back Matter

    Pages 168-173
    Download chapter PDF
Back to top

Keywords

About this book

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.

Bibliographic Information

  • Book Title: The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations

  • Authors: Jan Chabrowski

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095750

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54486-9Published: 25 September 1991

  • eBook ISBN: 978-3-540-38400-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 173

  • Topics: Analysis, Potential Theory, Fourier Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation