Bellman function for extremal problems in BMO
Analysis of PDEs
2016-04-07 v3 Classical Analysis and ODEs
Abstract
In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John--Nirenberg inequality and estimations of BMO functions. In the present paper we elaborate a method of solving the boundary value problem for the homogeneous Monge--Amp\`ere equation in a parabolic strip for sufficiently smooth boundary conditions. In such a way we have obtained an algorithm of constructing an exact Bellman function for a large class of integral functionals in the BMO space.
Cite
@article{arxiv.1205.7018,
title = {Bellman function for extremal problems in BMO},
author = {Paata Ivanisvili and Nikolay Osipov and Dmitriy Stolyarov and Vasily Vasyunin and Pavel Zatitskiy},
journal= {arXiv preprint arXiv:1205.7018},
year = {2016}
}
Comments
91 pages, 18 figures