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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
N. V. Krylov, University of Minnesota, Minneapolis, MN
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Graduate Studies in Mathematics
2008; 357 pp; hardcover
Volume: 96
ISBN-10: 0-8218-4684-1
ISBN-13: 978-0-8218-4684-1
List Price: US$67
Member Price: US$53.60
Order Code: GSM/96
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This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces.

The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with \(\mathsf{VMO}\) coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material.

After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequisites are basics of measure theory, the theory of \(L_p\) spaces, and the Fourier transform.

Readership

Graduate students and research mathematicians interested in partial differential equations.

Reviews

"This book is certain to become a source of inspiration for every researcher in nonlinear analysis. [The book] is beautifully written and well organized, and I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of the modern nonlinear analysis."

-- Mathematical Reviews

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