An introduction to second order partial differential equations : classical and variational solutions / Doina Cioranescu, Patrizia Donato, and Marian P. Roque.

Includes bibliographical references and index.

Classical partial differential equations -- What is a partial differential equation -- Classification of partial differential equations -- Elliptic equations -- Parabolic equations -- Variational partial differential equations -- L-spaces -- The sobolev spaces -- Sobolev embedding theorems -- Variational elliptic problems -- Variational evolution problems.

"The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs, that is, equations which admit strong solutions, verifying the equations pointwise. Classical solutions of the Laplace, heat, and wave equations are provided. Part II deals with variational PDEs, where weak (variational) solutions are considered. They are defined by variational formulations of the equations, based on Sobolev spaces. A comprehensive and detailed presentation of these spaces is given. Examples of variational elliptic, parabolic, and hyperbolic problems with different boundary conditions are discussed." -- Back cover