Lectures on elliptic and parabolic equations in Sobolev spaces
By: N.V. Krylov.
Series: Graduate studies in mathematics -- v. 96
Publisher: American Mathematical Society
Published: 2008
Place of publication: Providence, R.I
Language: eng
Number of pages: 357
ISBN-13: 9780821846841
Subjects: Differential equations, Elliptic; Differential equations, Parabolic; Sobolev spaces
Description: "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 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[subscript p] spaces, and the Fourier transform."--Jacket.
Notes: Includes bibliographical references and index.