Functional Analytic Methods for Partial Differential Equations

by Hiroki Tanabe

Overview

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.

Product Details

ISBN-13:	9780367401221
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Pages:	432
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Hiroki Tanabe is a Professor in the Department of Economics at Otemon Gakuin University, Osaka, Japan. The author of three books on functional analysis and evolution equations, he is a member of the Mathematical Society of Japan and the American Mathematical Society. Dr. Tanabe received the Ph.D. degree (1960) in mathematics from Osaka University, Japan.

Table of Contents

Singular integrals; Sobolev spaces; elliptic boundary value problems; elliptic boundary value problems (continued); parabolic evolution equations; hyperbolic evolution equations; retarded functional differential equations; list of symbols.

Editorial Reviews

This is an excellent monograph on the applications of functional analytic methods in partial differential equations. "Written by a recognized international expert, the book will be of great interest to mathematical analysts, physicists as well as graduate and postgraduate level students in the field.

Zentrallblatt fur Mathematik

Due to the large area of tackled problems and to the clear and detailed proofs, this monograph is interesting and accessible both to specialists and to graduate students.

Rev. Roumaine Math. Pures Appl. 2000

Presents detailed discussions on the applications of functional analytic methods in partial differential equations, combining both classical and current methods of analysis. Early chapters present a self-contained proof of Agmon-Douglis-Nireberg's Lp estimates for elliptic boundary value problems, with discussion of the theory of singular integrals and the Hilbert transform. The second half of the book is devoted to evolution equations in Banach spaces, with material on parabolic and hyperbolic equations, retarded functional differential equations, and related control theory. For mathematical analysts, geometers, mathematicians, physicists, and engineers. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"This is an excellent monograph on the applications of functional analytic methods in partial differential equations. Written by a recognized international expert, the book will be of great interest to mathematical analysts, physicists as well as graduate and postgraduate level students in the field. "
---Zentrallblatt fur Mathematik
"Due to the large area of tackled problems and to the clear and detailed proofs, this monograph is interesting and accessible both to specialists and to graduate students."
---Rev. Roumaine Math. Pures Appl., 2000

From the Publisher