Evans (Mathematics, University of California at Berkeley) provides a comprehensive survey of modern techniques in the theoretical study of partial differential equations, focusing particularly on nonlinear equations. The book has three parts: Part I covers representation formulas for solutions; Part II deals with theory for linear partial differential equations; and Part III explores theory for nonlinear partial differential equations. Topics include 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; and shock waves and entropy criteria for conservation laws. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)