Bellman function for extremal problems in BMO

By Paata Ivanisvili, Nikolay N. Osipov, D. Stolyarov, V. Vasyunin, P. Zatitskiy. 2012

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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 large class of integral functionals on the BMO space.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/ec81850b247ea7ef256daf2adc6df26dd0c580ad