Relative Rearrangement

By Jean Michel Rakotoson

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 P lya-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 R arrangement relatif: un instrument d'estimations dans les probl mes aux limites (Springer, 2008), this edition contains additional recent results and new exercises concerning interpolation theory.

• Format: Paperback
• Language: English
• ISBN: 3032022274
• ISBN13: 9783032022271
• Release Date: October 2025
• Publisher: Springer
• Length: 414 Pages
• Weight: 1.33 lbs.
• Dimensions: 0.9" x 6.1" x 9.2"