Bellman function for extremal problems in BMO

@article{Ivanisvili2012BellmanFF,
  title={Bellman function for extremal problems in BMO},
  author={Paata Ivanisvili and Nikolay N. Osipov and Dmitriy M. Stolyarov and Vasily I. Vasyunin and Pavel Zatitskiy},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={368},
  pages={3415-3468}
}
In this paper we develop the method of nding 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{Amp ere equation in a parabolic strip for suciently smooth boundary conditions. In such a way, we have obtained an algorithm for constructing an exact Bellman function for a… 
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