Skip to main content
SpringerLink
Log in

Partial Differential Equations III

Nonlinear Equations

  • Textbook
  • © 2023

Overview

Authors:
  1. Michael E. Taylor

    1. Department of Mathematics, University of North Carolina, Chapel Hill, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Three volumes offer complete reference to PDE's
  • Includes both theory and applications
  • Lots of examples and exercises

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

  • 2685 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 84.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxiii
    Download chapter PDF

  2. Function Space and Operator Theory for Nonlinear Analysis

    • Michael E. Taylor
    Pages 1-106

  3. Nonlinear Elliptic Equations

    • Michael E. Taylor
    Pages 107-334

  4. Nonlinear Parabolic Equations

    • Michael E. Taylor
    Pages 335-433

  5. Nonlinear Hyperbolic Equations

    • Michael E. Taylor
    Pages 435-552

  6. Euler and Navier–Stokes Equations for Incompressible Fluids

    • Michael E. Taylor
    Pages 553-654

  7. Einstein’s Equations

    • Michael E. Taylor
    Pages 655-749

  8. Back Matter

    Pages 751-755
    Download chapter PDF
Back to top

Keywords

About this book

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. 

The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters.  It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids.  The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.

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.”

(Peter Lax, SIAM review, June 1998)


Authors and Affiliations

  • Department of Mathematics, University of North Carolina, Chapel Hill, USA

    Michael E. Taylor

About the author

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/10.1007/978-3-031-33928-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-33927-1Published: 07 December 2023

  • Softcover ISBN: 978-3-031-33930-1Due: 07 January 2024

  • eBook ISBN: 978-3-031-33928-8Published: 06 December 2023

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 3

  • Number of Pages: XXIII, 755

  • Number of Illustrations: 65 b/w illustrations

  • Topics: Partial Differential Equations

Publish with us

Policies and ethics

Back to top

Search

Navigation