Partial differential equations

(Graduate studies in mathematics) Summary: "This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including: a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, and a significantly expanded bibliography."--Publisher's description

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PART I. REPRESENTATION FORMULAS FOR SOLUTIONS: Four important linear PDE. Nonlinear first-order PDE. Other ways to represent solutions. PART II. THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS: Sobolev spaces. Second-order elliptic equations. Linear evolution equations. PART III. THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS: The calculus of variations. Nonvariational techniques. Hamilton-Jacobi equations. Systems of conservation laws. Nonlinear wave equations

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