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arXiv · 1205.7018

Bellman function for extremal problems in BMO

Paata Ivanisvili·Nikolay Osipov·Dmitriy Stolyarov·Vasily Vasyunin·Pavel Zatitskiy
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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 $L^p$ estimations of BMO functions. In the present paper we elaborate a method of solving the boundary value problem for the homogeneous Monge--Ampère 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.

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Paata Ivanisvili, Nikolay Osipov, Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy. 2012-12-10. Bellman function for extremal problems in BMO. https://arxiv.org/abs/1205.7018

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