Geodesic
An example of constructing the Bellman function for extremal problems in BMO
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 33-125

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An example of solution of a boundary value problem for a homogeneous Monge–Ampère equation is given, which produces a Bellman function for an extremal problem on the space BMO. The paper contains a step-by-step instruction for calculation of this function. The cases of a rather complicated foliation are considered. This illustrates the technique elaborated in a paper by Ivanishvili, Stoyanov, Vasyunin, and Zatitsky. 
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     author = {V. I. Vasyunin},
     title = {An example of constructing the {Bellman} function for extremal problems in {BMO}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--125},
     publisher = {mathdoc},
     volume = {424},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a1/}
}
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V. I. Vasyunin. An example of constructing the Bellman function for extremal problems in BMO. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 33-125. http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a1/