Partial Differential EquationsThis 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 secondorder elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of HamiltonJacobi 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 calculustype estimates within the context of Sobolev spaces. Treatment of all topics is complete and selfcontained. 
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LibraryThing Review
User Review  PDExperiment626  LibraryThingI've seen a lot of positive reviews of this text, and I feel the need to explain some cons of this book. Before that, I will say this is probably the best introduction to PDE theory out there. This is ... Read full review
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An excellent treatment of the topic.