Analytic Semigroups and Optimal Regularity in Parabolic Problems

Nachdruck of the 1. Auflage 1995 by Birkhäuser Verlag, Switzerland 2012
ISBN: 978-3-0348-0556-8
Verlag: Springer

Buch, Englisch, 424 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 668 g

Reihe: Modern Birkhäuser Classics

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.

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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)

Zielgruppe

Research

Autoren/Hrsg.

Lunardi, Alessandra

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Introduction.- 0 Preliminary material: spaces of continuous and Hölder continuous functions.- 1 Interpolation theory.- Analytic semigroups and intermediate spaces.- 3 Generation of analytic semigroups by elliptic operators.- 4 Nonhomogeneous equations.- 5 Linear parabolic problems.- 6 Linear nonautonomous equations.- 7 Semilinear equations.- 8 Fully nonlinear equations.- 9 Asymptotic behavior in fully nonlinear equations.- Appendix: Spectrum and resolvent.- Bibliography.- Index.

Über Autor(innen)

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