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Wave Factorization of Elliptic Symbols: Theory and Applications

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

  • Book
  • © 2000

Overview

Authors:
  1. Vladimir B. Vasil’ev

    1. Department of Mathematical Analysis, Novgorod State University, Novgorod, Russia

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Distributions and Their Fourier transforms

    • Vladimir B. Vasil’ev
    Pages 1-7

  3. Multidimensional complex analysis

    • Vladimir B. Vasil’ev
    Pages 7-13

  4. Sobolev-Slobodetskii spaces

    • Vladimir B. Vasil’ev
    Pages 13-17

  5. Pseudodifferential operators and equations in a half-space

    • Vladimir B. Vasil’ev
    Pages 17-26

  6. Wave factorization

    • Vladimir B. Vasil’ev
    Pages 27-36

  7. Diffraction on a quadrant

    • Vladimir B. Vasil’ev
    Pages 36-42

  8. The problem of indentation of a wedge-shaped punch

    • Vladimir B. Vasil’ev
    Pages 42-50

  9. Equations in an infinite plane angle

    • Vladimir B. Vasil’ev
    Pages 51-67

  10. General boundary value problems

    • Vladimir B. Vasil’ev
    Pages 67-83

  11. The Laplacian in a plane infinite angle

    • Vladimir B. Vasil’ev
    Pages 84-105

  12. Problems with potentials

    • Vladimir B. Vasil’ev
    Pages 105-113

  13. Back Matter

    Pages 114-176
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematical Analysis, Novgorod State University, Novgorod, Russia

    Vladimir B. Vasil’ev

Bibliographic Information

  • Book Title: Wave Factorization of Elliptic Symbols: Theory and Applications

  • Book Subtitle: Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains

  • Authors: Vladimir B. Vasil’ev

  • DOI: https://doi.org/10.1007/978-94-015-9448-6

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 2000

  • Hardcover ISBN: 978-0-7923-6531-0Published: 30 September 2000

  • Softcover ISBN: 978-90-481-5545-3Published: 04 December 2010

  • eBook ISBN: 978-94-015-9448-6Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: X, 176

  • Topics: Partial Differential Equations, Functional Analysis, Analysis, Integral Equations, Operator Theory, Classical Mechanics

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