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Bellman Function for Extremal Problems in BMO II: Evolution

About this Title

Paata Ivanisvili, Kent State University, Kent, Ohio 44243, Dmitriy M. Stolyarov, Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178, Russia – and – St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg, 191023, Russia, Vasily I. Vasyunin, St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg, 191023, Russia – and – Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178, Russia and Pavel B. Zatitskiy, Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178, Russia – and – St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg, 191023, Russia

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)
DOI: https://doi.org/10.1090/memo/1220
Published electronically: August 2, 2018
Keywords: Bellman function, bounded mean oscialltion
MSC: Primary 42B35, 26D07, 52A10, 35E10

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Table of Contents

Chapters

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

Abstract

In a previous study, the authors built the Bellman function for integral functionals on the $\mathrm {BMO}$ 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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