An Example of Constructing a Bellman Function for Extremal Problems in BMO

被引：0
作者：
Vasyunin V.I. [1 ]
机构：
[1] St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg
来源：
Journal of Mathematical Sciences | 2015年 / 209卷 / 5期
关键词：
Balance Equation; Tangent Line; Bellman Function; Extremal Line; Positive Semiaxis;
D O I：
10.1007/s10958-015-2521-3
中图分类号：
学科分类号：
摘要：
An example of solving 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. Cases of rather complicated foliations are considered. This illustrates the technique elaborated in a paper by Ivanishvili, Stolyarov, Vasyunin, and Zatitskiy. Bibliography: 6 titles. © 2015, Springer Science+Business Media New York.
引用
收藏
页码：683 / 742
页数：59
相关论文
共 6 条
  • [1] Ivanishvili P., Osipov N., Stolyarov D., Vasyunin V., Zatitskiy P., On Bellman function for extremal problems in BMO, Comptes Rendus Mathematique, 350, pp. 561-564, (2012)
  • [2] Ivanishvili P., Osipov N., Stolyarov D., Vasyunin V., Zatitskiy P., Bellman function for extremal problems in BMO, Trans. Amer. Math. Soc
  • [3] Vasyunin V.I., Zatitskiy P.B., Ivanishvili P., Osipov N.N., Stolyarov D.M., Bellman function in BMO space,, PDMI preprint, 19, pp. 1-101, (2011)
  • [4] Vasyunin V.I., Zatitskiy P.B., Ivanishvili P., Osipov N.N., Stolyarov D.M., Addendum to PDMI preprint 19/2011 ‘Bellman function in BMO space’,, PDMI Preprint, 10, pp. 1-15, (2012)
  • [5] Ivanishvili P., Osipov N., Stolyarov D., V. Vasyunin, and P, Zatitskiy, “Bellman function for extremal problems in BMO,” arXiv:1205.7018v3, pp. 1-91, (2012)
  • [6] Ivanishvili P., Stolyarov D., Vasyunin V., Zatitskiy P., Bellman function for extremal problems in BMO: evolution
1