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Bellman Function for Extremal Problems in BMO II: Evolution

About this Title

Paata Ivanisvili, Dmitriy M. Stolyarov, Vasily I. Vasyunin and Pavel B. Zatitskiy

Publication: Memoirs of the American Mathematical Society
Publication Year: 2018; Volume 255, Number 1220
ISBNs: 978-1-4704-2954-6 (print); 978-1-4704-4817-2 (online)
Published electronically: August 2, 2018
Keywords:Bellman function, bounded mean oscialltion

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Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. Setting and sketch of proof
  • Chapter 3. Patterns for Bellman candidates
  • Chapter 4. Evolution of Bellman candidates
  • Chapter 5. Optimizers
  • Chapter 6. Related questions and further development


In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. We abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows us to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, evolution of its picture

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