Analytic Semigroups and Optimal Regularity in Parabolic Problems

Authors: Alessandra Lunardi



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

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)

Table of contents

Preliminary material: spaces of continuous and Hölder continuous functions

Interpolation theory

Analytic semigroups and intermediate spaces

Generation of analytic semigroups by elliptic operators

Nonhomogeneous equations

Linear parabolic problems

Linear nonautonomous equations

Semilinear equations

Fully nonlinear equations

Asymptotic behavior in fully nonlinear equations