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  • © 1988

Elliptic Boundary Value Problems on Corner Domains

Smoothness and Asymptotics of Solutions

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1341)

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  • ISBN: 978-3-540-45942-2
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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VIII
  2. Introduction

    • Monique Dauge
    Pages 2-7
  3. Preliminaries

    • Monique Dauge
    Pages 8-24
  4. Fredholm and semi-Fredholm results

    • Monique Dauge
    Pages 26-57
  5. Proofs

    • Monique Dauge
    Pages 58-103
  6. Two-dimensional domains

    • Monique Dauge
    Pages 104-127
  7. Singularities along the edges

    • Monique Dauge
    Pages 128-152
  8. Laplace operator

    • Monique Dauge
    Pages 153-170
  9. Back Matter

    Pages 214-261

About this book

This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic theory (new approaches and results) as well as a synthesis of many already known results; those who need regularity conditions and descriptions of singularities for numerical analysis will find precise statements and also a means to obtain further one in many explicit situtations.

Keywords

  • BVP
  • Boundary value problem
  • Laplace operator
  • Smooth function
  • Sobolev space
  • operator

Bibliographic Information

  • Book Title: Elliptic Boundary Value Problems on Corner Domains

  • Book Subtitle: Smoothness and Asymptotics of Solutions

  • Authors: Monique Dauge

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0086682

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50169-5

  • eBook ISBN: 978-3-540-45942-2

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 264

  • Topics: Analysis

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-45942-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 59.99
Price excludes VAT (USA)