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Relative rearrangement

Record Type:	Electronic resources : Monograph/item
Title/Author:	Relative rearrangementby Jean Michel Rakotoson.
Author:	Rakotoson, Jean-Michel.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xvi, 414 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations.
Online resource:	https://doi.org/10.1007/978-3-032-02228-8
ISBN:	9783032022288$q(electronic bk.)

Relative rearrangement
Rakotoson, Jean-Michel.

Relative rearrangement[electronic resource] /by Jean Michel Rakotoson. - Cham :Springer Nature Switzerland :2025. - xvi, 414 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 223761617-9692 ;. - Lecture notes in mathematics ;2035..

Chapter 1. Monotone Rearrangement -- Chapter 2. Relative Rearrangement -- Chapter 3. Polya-Szego inequalities and regularity of monotone rearrangement -- Chapter 4. Pointwise inequalities and Sobolev inclusions -- Chapter 5. Formalism of estimates for boundary value problems -- Chapter 6. Continuity of the derivative map of the monotone rearrangement -- Chapter 7. Strong continuity of the relative rearrangement map u ! b*u and consequences -- Chapter 8. Some problems related to relative rearrangement -- Chapter 9. Time-dependent functions and evolution equations -- Chapter 10. Relative rearrangement and Lebesgue spaces with variable exponents -- Chapter 11. Exercises and Problems.

This book develops the properties of monotone rearrangement and relative rearrangement (sometimes called pseudo-rearrangement). It introduces applications to variational problems involving monotone rearrangements, a priori estimates for partial differential equations, and stationary or evolution problems associated with variable exponents. The properties of Sobolev embeddings for non-standard spaces such as BMO, VMO, Zygmung spaces and more general spaces invariant under rearrangement are also reviewed. The book is relatively self-contained - elementary details for non-specialists are covered in the first chapter, including, among other things, some punctual inequalities for the Sobolev embeddings and Pólya-Szegő type inequalities, which lead, for instance, to explicit and even precise estimates. The final chapter includes numerous exercises, with solutions. Based on the author's Réarrangement relatif: un instrument d'estimations dans les problèmes aux limites (Springer, 2008), this edition contains additional recent results and new exercises concerning interpolation theory.

ISBN: 9783032022288$q(electronic bk.)

Standard No.: 10.1007/978-3-032-02228-8doiSubjects--Topical Terms:

183925
Differential equations.

LC Class. No.: QA379

Dewey Class. No.: 515.35

Relative rearrangement
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520 $a This book develops the properties of monotone rearrangement and relative rearrangement (sometimes called pseudo-rearrangement). It introduces applications to variational problems involving monotone rearrangements, a priori estimates for partial differential equations, and stationary or evolution problems associated with variable exponents. The properties of Sobolev embeddings for non-standard spaces such as BMO, VMO, Zygmung spaces and more general spaces invariant under rearrangement are also reviewed. The book is relatively self-contained - elementary details for non-specialists are covered in the first chapter, including, among other things, some punctual inequalities for the Sobolev embeddings and Pólya-Szegő type inequalities, which lead, for instance, to explicit and even precise estimates. The final chapter includes numerous exercises, with solutions. Based on the author's Réarrangement relatif: un instrument d'estimations dans les problèmes aux limites (Springer, 2008), this edition contains additional recent results and new exercises concerning interpolation theory.
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