Bellman Function for Extremal Problems in BMO II: Evolution ( Memoirs of the American Mathematical Society )

Publication series ： Memoirs of the American Mathematical Society

Author： Paata Ivanisvili;Dmitriy M. Stolyarov;Vasily I. Vasyunin

Publisher： American Mathematical Society‎

Publication year： 2018

E-ISBN: 9781470448172

P-ISBN(Paperback): 9781470429546

Subject： O1 Mathematics

Keyword：数学

Language： ENG

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Bellman Function for Extremal Problems in BMO II: Evolution

Description

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. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.

Chapter

Cover

Title page

Chapter 1. Introduction

1.1. Historical remarks

1.2. Structure of the paper

Chapter 2. Setting and sketch of proof

2.1. Setting

2.2. On concavity of surfaces and functions

Chapter 3. Patterns for Bellman candidates

3.1. Preliminaries

3.2. Tangent domains

3.3. Around the cup

3.4. Linearity domains

3.5. Combinatorial properties of foliations

Chapter 4. Evolution of Bellman candidates

4.1. Simple picture

4.2. Preparation to evolution

4.3. Local evolutional theorems

4.4. Global evolution

4.5. Examples

Chapter 5. Optimizers

5.1. Abstract theory

5.2. Local behavior of optimizers

5.3. Global optimizers

5.4. Examples

Chapter 6. Related questions and further development

6.1. Related questions

6.2. Further development

Bibliography

Index

Back Cover

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