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© 2011

Partial Differential Equations III

Nonlinear Equations

Book

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

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

About the authors

Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.

Bibliographic information

  • Book Title Partial Differential Equations III
  • Book Subtitle Nonlinear Equations
  • Authors Michael E. Taylor
  • Series Title Applied Mathematical Sciences
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-7048-0
  • Softcover ISBN 978-1-4614-2741-4
  • eBook ISBN 978-1-4419-7049-7
  • Series ISSN 0066-5452
  • Series E-ISSN 2196-968X
  • Edition Number 2
  • Number of Pages XXII, 715
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
  • Buy this book on publisher's site
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Reviews

From the reviews:

“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)

From the reviews of the second edition:

“This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. … Graduate students … will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. … an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics.” (Christian Constanda, The Mathematical Association of America, July, 2011)