Partial Differential Equations II

Qualitative Studies of Linear Equations

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 116)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Michael E. Taylor
    Pages 1-90
  3. Michael E. Taylor
    Pages 91-173
  4. Michael E. Taylor
    Pages 175-280
  5. Michael E. Taylor
    Pages 281-360
  6. Michael E. Taylor
    Pages 361-456
  7. Michael E. Taylor
    Pages 457-537
  8. Michael E. Taylor
    Pages 539-609
  9. Back Matter
    Pages 611-614

About this book

Introduction

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time.

Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(SIAM Review, June 1998)

Keywords

Brownian Motion Potential Theory Pseudodifferential Operators Scattering by Obstacles Spectral Theory

Authors and affiliations

  • Michael E. Taylor
    • 1
  1. 1., Department of MathematicsUniversity of North CarolinaChapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7052-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7051-0
  • Online ISBN 978-1-4419-7052-7
  • Series Print ISSN 0066-5452
  • About this book