Analytic semigroups and optimal regularity in parabolic problems
著者
書誌事項
Analytic semigroups and optimal regularity in parabolic problems
（Progress in nonlinear differential equations and their applications / editor, Haim Brezis, v. 16）
Birkhäuser, 1995
- : sz
- : us
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 Holder continuous derivatives. (Zentralblatt MATH)
目次
Introduction.- 0 Preliminary material: spaces of continuous and Holder 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.
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