Lectures On Elliptic And Parabolic Equations In Sobolev Spaces
N. V. Krylov
ISBN 10: 1470479788 ISBN 13: 9781470479787
Published by American Mathematical Society, 2024
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Soft cover
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Synopsis:
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.
About the Author: N. V. Krylov, University of Minnesota, Minneapolis, MN.
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Bibliographic Details
Title: Lectures On Elliptic And Parabolic Equations...
Publisher: American Mathematical Society
Publication Date: 2024
Binding: Soft cover
Condition: New