Partial differential equations. III, Nonlinear equations / Michael E. Taylor.
2023
QA372
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Details
Title
Partial differential equations. III, Nonlinear equations / Michael E. Taylor.
Edition
Third edition.
ISBN
9783031339288 (electronic bk.)
3031339282 (electronic bk.)
9783031339271
3031339274
3031339282 (electronic bk.)
9783031339271
3031339274
Published
Cham : Springer, 2023.
Language
English
Description
1 online resource (734 pages) : illustrations (black and white).
Other Standard Identifiers
10.1007/978-3-031-33928-8 doi
Call Number
QA372
Dewey Decimal Classification
515/.355
Summary
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).
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Description based on print version record.
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 117.
Available in Other Form
Partial differential equations. III, Nonlinear equations.
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Table of Contents
Contents of Volumes I and II
Preface
13 Function Space and Operator Theory for Nonlinear Analysis
14 Nonlinear Elliptic Equations
15 Nonlinear Parabolic Equations
16 Nonlinear Hyperbolic Equations
17 Euler and NavierStokes Equations for Incompressible Fluids
18 Einsteins Equations
Index.
Preface
13 Function Space and Operator Theory for Nonlinear Analysis
14 Nonlinear Elliptic Equations
15 Nonlinear Parabolic Equations
16 Nonlinear Hyperbolic Equations
17 Euler and NavierStokes Equations for Incompressible Fluids
18 Einsteins Equations
Index.