Partial Differential Equations III: Nonlinear Equations

This book is a comprehensive treatment of nonlinear partial differential equations,covering classical continuum mechanics,differential geometry,and diffusion problems. It introduces analytical tools such as L^p Sobolev spaces,Holder spaces,Hardy spaces,and Morrey spaces,and develops the Calderon-Zygmund theory and paradifferential operator calculus. It is aimed at graduate students and professional mathematicians with an interest in partial differential equations,mathematical physics,differential geometry,harmonic analysis,and complex analysis.

Format: Hardback
Length: 755 pages
Publication date: 07 December 2023
Publisher: Springer International Publishing AG

This is the third of three volumes on partial differential equations, dedicated 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 Lp 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.”

Weight: 1442g
Dimension: 162 x 244 x 44 (mm)
ISBN-13: 9783031339271
Edition number: 3rd ed. 2023