Partial Differential Equations (Graduate Studies in Mathematics, Vol. 19) - Hardcover

Evans, Lawrence C.

Hardcover

ISBN 10: 0821807722 ISBN 13: 9780821807729

Publisher: Amer Mathematical Society, 1998

Synopsis

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partial differential equations, and 3) theory for nonlinear partial differential equations.

Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and much more.

The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he emphasizes the modern interplay between functional analytic insights and calculus-type estimates within the context of Sobolev spaces. Treatment of all topics is complete and self-contained. The book's wide scope and clear exposition make it a suitable text for a graduate course in PDEs.

About this title

Review:

"...Highly recommend the book for students as well as for lectures in PDE." -- Monatshefte fur Mathematik

"...entirely possible that the ...text could eventually become the benchmark. ...extremely well written..." -- SIAM Review

"For a student wishing to specialise in the theory of PDEs it provides a very solid foundation." -- The Mathematical Gazette

"Highly recommend the book for students as well as for lectures in PDE." -- Monatshefte fr Mathematik

"It is a standard treatment with good notation. It is extremely well written, with a very attractive format." -- SIAM Review

"This excellent textbook [is recommended] as the first textbook for anyone who wants to learn the theory of [PDE]" -- European Mathematical Society Newsletter

"Well written; proofs are given in full detail and pictures are inserted when needed; moreover, the exposition is perfectly self-contained, the development within each part and section being rigorous and complete." -- Mathematical Reviews

For a student wishing to specialise in the theory of PDEs it provides a very solid foundation. -- The Mathematical Gazette

About this edition

• Publisher: Amer Mathematical Society
• Publication date: 1998
• ISBN 10: 0821807722
• ISBN 13: 9780821807729
• Binding: Hardcover
• Edition number: 1
• Number of pages: 662