Modern Birkhäuser Classics

Analytic Semigroups and Optimal Regularity in Parabolic Problems

Authors: Lunardi, Alessandra

  • Systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces
  • Known Theorems are presented from a novel perspective
  • Teaches how to exploit basic techniques
  • Addresses PhD students as well as researchers​
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Softcover $99.00
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  • ISBN 978-3-0348-0556-8
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About this book

The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems.

Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones.

Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived.

The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.

- - -

This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems.
(Mathematical Reviews)  

Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives.
(Zentralblatt MATH)

About the authors

Alessandra Lunardi is a professor of mathematics at the University of Parma, Italy.

Table of contents (10 chapters)

  • Preliminary material: spaces of continuous and Hölder continuous functions

    Lunardi, Alessandra

    Pages 1-10

  • Interpolation theory

    Lunardi, Alessandra

    Pages 11-32

  • Analytic semigroups and intermediate spaces

    Lunardi, Alessandra

    Pages 33-67

  • Generation of analytic semigroups by elliptic operators

    Lunardi, Alessandra

    Pages 69-119

  • Nonhomogeneous equations

    Lunardi, Alessandra

    Pages 121-171

Buy this book

Softcover $99.00
price for USA
  • ISBN 978-3-0348-0556-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Analytic Semigroups and Optimal Regularity in Parabolic Problems
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1995
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
Softcover ISBN
978-3-0348-0556-8
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XVII, 424
Additional Information
Originally published as volume 16in the series: Progress in Nonlinear Differential Equations and Their Applications series
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