This masterful text introduces first-year graduate students to the basic ideas of the theory of partial differential equations in the context of the three fundamental equations of classical mathematical physics - the wave and heat equations and the Laplace equation. The authors avoid abstractions and succeed in demonstrating ideas by way of relatively simple, straightforward applications. Their book also deals with more advanced topics, including - the De Giorgi-Nash-Moser theorem - nonlinear Dirichlet problems for elliptic equations - distributions and Sobolev spaces - and hyperbolic conservation laws in one space variable.
Introduces basic ideas of the theory of partial differential equations in the context of the three fundamental equations of classical mathematical physics: the wave, heat, and laplace equations. Avoids abstractions and generalizations in order to demonstrate ideas in straightforward situations and relevant applications. Coverage includes elliptic second-order partial differential equations, abstract evolution equations, distributions and Sobolev spaces, and a proof of existence by Glimm's Random Choice Method. Advanced topics include Dirichlet problems for nonlinear elliptic equations. Includes chapter exercises. For first-year graduate students in mathematics. Also useful for students in aerospace and mechanical engineering. Annotation c. by Book News, Inc., Portland, Or.