Cioranescu D., Donato P., Roque M.P. An introduction to second order partial differential equations. Classical and variational solutions

Singapore: World Scientific Publishing Company, 2017. — 301 p. — ISBN: 978-9813229174.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.List of Symbols
Classical Partial Differential Equations:
What is a Partial Differential Equation?
Classification of Partial Differential Equations
Elliptic Equations
Parabolic Equations
Hyperbolic Equations
Variational Partial Differential Equations:
Lp-spaces
The Sobolev Spaces W1,p
Sobolev Embedding Theorems
Variational Elliptic Problems
Variational Evolution ProblemsReadership: Graduate and post-graduate students as well as researchers who are interested in PDEs in both classical and variational approaches.
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