Wave Factorization of Elliptic Symbols: Theory and Applications

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

Authors: Vasil'ev, V.

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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.

Table of contents (11 chapters)

  • Distributions and Their Fourier transforms

    Vasil’ev, Vladimir B.

    Pages 1-7

  • Multidimensional complex analysis

    Vasil’ev, Vladimir B.

    Pages 7-13

  • Sobolev-Slobodetskii spaces

    Vasil’ev, Vladimir B.

    Pages 13-17

  • Pseudodifferential operators and equations in a half-space

    Vasil’ev, Vladimir B.

    Pages 17-26

  • Wave factorization

    Vasil’ev, Vladimir B.

    Pages 27-36

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-94-015-9448-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-0-7923-6531-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-90-481-5545-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-9448-6
DOI
10.1007/978-94-015-9448-6
Hardcover ISBN
978-0-7923-6531-0
Softcover ISBN
978-90-481-5545-3
Edition Number
1
Number of Pages
X, 176
Topics