Analytic Semigroups and Optimal Regularity in Parabolic Problems by Alessandra LunardiAnalytic Semigroups and Optimal Regularity in Parabolic Problems by Alessandra Lunardi

Analytic Semigroups and Optimal Regularity in Parabolic Problems

byAlessandra Lunardi

Paperback | December 14, 2012

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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)

Alessandra Lunardi is a professor of mathematics at the University of Parma, Italy.
Title:Analytic Semigroups and Optimal Regularity in Parabolic ProblemsFormat:PaperbackDimensions:424 pages, 23.5 × 15.5 × 0.01 inPublished:December 14, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:303480556X

ISBN - 13:9783034805568


Table of Contents

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.?