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Partial Differential Equations
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Partial Differential Equations

Partial Differential Equations

Lawrence C. Evans - Collection Graduate Studies in Mathematics

662 pages, parution le 31/08/2004


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 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.


  • Introduction
  • Representation formulas for solutions
  • Theory for linear partial differential equations
  • Theory for nonlinear partial differential equations
  • Appendices
  • Bibliography
  • Index
Voir tout

Caractéristiques techniques

Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Lawrence C. Evans
Collection Graduate Studies in Mathematics
Parution 31/08/2004
Nb. de pages 662
Couverture Relié
Poids 1388g
Intérieur Noir et Blanc
EAN13 9780821807729
ISBN13 978-0-821-80772-9

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