Lecture Notes in Mathematics

Rakotoson, Jean Michel

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. 

Details

Published by: Springer

Publication Date: 2025-10-28

Format: Paperback

ISBN-13: 9783032022271

DOI: 10.1007/978-3-032-02228-8

Dimensions: 235cm x155cm

Pages: 414