Partial Differential Equations III

Nonlinear Equations

  • Michael E. Taylor

Part of the Applied Mathematical Sciences book series (AMS, volume 117)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Michael E. Taylor
    Pages 105-311
  3. Michael E. Taylor
    Pages 313-411
  4. Michael E. Taylor
    Pages 413-529
  5. Michael E. Taylor
    Pages 615-709
  6. Back Matter
    Pages 711-715

About this book

Introduction

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. 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, an extension of complex interpolation theory, and Navier-Stokes equations with small viscosity. 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

Einstein's equations Navier-Stokes equations Nonlinear elliptic equations Nonlinear hyperbolic equations

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7049-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7048-0
  • Online ISBN 978-1-4419-7049-7
  • Series Print ISSN 0066-5452
  • About this book