Wave Factorization of Elliptic Symbols: Theory and Applications

Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains

  • Vladimir B. Vasil’ev

Table of contents

  1. Front Matter
    Pages i-ix
  2. Vladimir B. Vasil’ev
    Pages 1-7
  3. Vladimir B. Vasil’ev
    Pages 7-13
  4. Vladimir B. Vasil’ev
    Pages 13-17
  5. Vladimir B. Vasil’ev
    Pages 27-36
  6. Vladimir B. Vasil’ev
    Pages 36-42
  7. Vladimir B. Vasil’ev
    Pages 42-50
  8. Vladimir B. Vasil’ev
    Pages 51-67
  9. Vladimir B. Vasil’ev
    Pages 67-83
  10. Vladimir B. Vasil’ev
    Pages 84-105
  11. Vladimir B. Vasil’ev
    Pages 105-113
  12. Back Matter
    Pages 114-176

About this book

Introduction

To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains. The elements of such a theory already exist in the literature and can be found in such papers and monographs as [90,95,96,109,115,131,132,134,135,136,146, 163,165,169,170,182,184,214-218]. In this book, we will employ a theory that is based on quite different principles than those used previously. However, precisely one of the standard principles is left without change, the "freezing of coefficients" principle. The first main difference in our exposition begins at the point when the "model problem" appears. Such a model problem for differential equations and differential boundary conditions was first studied in a fundamental paper of V. A. Kondrat'ev [134]. Here also the second main difference appears, in that we consider an already given boundary value problem. In some transformations this boundary value problem was reduced to a boundary value problem with a parameter . -\ in a domain with smooth boundary, followed by application of the earlier results of M. S. Agranovich and M. I. Vishik. In this context some operator-function R('-\) appears, and its poles prevent invertibility; iffor differential operators the function is a polynomial on A, then for pseudo differential operators this dependence on . -\ cannot be defined. Ongoing investigations of different model problems are being carried out with approximately this plan, both for differential and pseudodifferential boundary value problems.

Keywords

Boundary value problem Distribution Fourier transform Operator theory Potential Singular integral partial differential equation

Authors and affiliations

  • Vladimir B. Vasil’ev
    • 1
  1. 1.Department of Mathematical AnalysisNovgorod State UniversityNovgorodRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9448-6
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5545-3
  • Online ISBN 978-94-015-9448-6
  • About this book