Partial Differential Equations

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: representation formulas for solutions; theory for linear partial differential equations; and 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 primarily 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.

ISBN 0821807722   Pages 712 ISBN13 9780821807729 (What's this?)   Volumes 000 Publisher American Mathematical Society   Weight (grammes) 1405 Imprint American Mathematical Society   Published in Providence Format Hardback   Series title Graduate Studies in Mathematics Publication date 15 May 1998   Height (mm) 267 Non-book description xvii, 662 p. :   Width (mm) 190 Library of Congress QA377.E95   Spine width (mm) 36 DEWEY 515.353   Academic level Professional / Scholarly DEWEY edition DC21

		Preface
1		Introduction		1
Pt. I		Representation Formulas for Solutions
2		Four Important Linear PDE		17
3		Nonlinear First-Order PDE		91
4		Other Ways to Represent Solutions		167
Pt. II		Theory for Linear Partial Differential Equations
5		Sobolev Spaces		239
6		Second-Order Elliptic Equations		293
7		Linear Evolution Equations		349
Pt. III		Theory for Nonlinear Partial Differential Equations
8		The Calculus of Variations		431
9		Nonvariational Techniques		491
10		Hamilton - Jacobi Equations		539
11		Systems of Conservation Laws		567
		App. A: Notation		613
App. B		Inequalities		621
App. C		Calculus Facts		626
App. D		Linear Functional Analysis		635
App. E		Measure Theory		645
		Bibliography
		Index		655

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