Relative Rearrangement

von Jean Michel Rakotoson

414 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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. 

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783032022271
• Sprache: Englisch
• Erscheinungsdatum: 28.10.2025
• Genre: Mathematik/Analysis
• Verlag: Springer International Publishing