Partial Differential Equations III by Taylor, Michael E.;

Nonlinear Equations

Series: Applied Mathematical Sciences; 117;

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Product details:

Edition number 3
Publisher Springer International Publishing
Date of Publication 25 December 2024
Number of Volumes 1 pieces, Book

ISBN 9783031339301
Binding Paperback
See also 9783031339271
No. of pages755 pages
Size 235x155 mm
Language English
Illustrations XXIII, 755 p. 65 illus. Illustrations, black & white

Long description:

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)

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 Navier–Stokes Equations for Incompressible Fluids.- 18 Einstein’s Equations.- Index.

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