Geodesic
Bellman function for a parametric family of extremal problems in $\mathrm{BMO}$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 128-142 
N. N. Osipov. Bellman function for a parametric family of extremal problems in $\mathrm{BMO}$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 128-142. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a11/
@article{ZNSL_2018_467_a11,
     author = {N. N. Osipov},
     title = {Bellman function for a~parametric family of extremal problems in~$\mathrm{BMO}$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {128--142},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a11/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Suppose $I$ is an interval on the real line and $\langle\cdot\rangle_I$ is the corresponding integral average. We describe how the Bellman function for the functional $F(\varphi)=\langle f\circ\varphi\rangle_I$, $\varphi\in\mathrm{BMO}(I)$, varies when $f$ runs over a certain parametric family of functions. Thereby, we once again demonstrate the work of the methods developed recently by V. I. Vasyunin, P. B. Zatitskiy, P. Ivanishvili, D. M. Stolyarov, and the author.

[1] P. Ivanishvili, N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, “Bellman function for extremal problems in $\mathrm{BMO}$”, Trans. Amer. Math. Soc., 368 (2016), 3415–3468 ; Препринт No 19, ПОМИ, 2011; Препринт No 10, ПОМИ, 2012 | DOI | MR

[2] P. Ivanisvili, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Bellman function for extremal problems in $\mathrm{BMO}$. II: evolution, Memoirs Amer. Math. Soc., 255, no. 1220, 2018 ; Препринт, arXiv: 1510.01010 | DOI | MR

[3] V. I. Vasyunin, “Primer postroeniya funktsii Bellmana dlya ekstremalnykh zadach v prostranstve $\mathrm{BMO}$”, Zap. nauchn. semin. POMI, 424, 2014, 33–125 | MR