Monge--Ampère equation and Bellman optimization of Carleson Embedding Theorems Export

@misc{citeulike:2565757, abstract = {Monge--Amp\`ere equation plays an important part in Analysis. For example, it is instrumental in mass transport problems. On the other hand, the Bellman function technique appeared recently as a way to consider certain Harmonic Analysis problems as the problems of Stochastic Optimal Control. This brings us to Bellman PDE, which in stochastic setting is often a Monge--Amp\`ere equation or its close relative. We explore the way of solving Monge--Amp\`ere equation by a sort of method of characteristics to find the Bellman function of certain classical Harmonic Analysis problems, and, therefore, of finding full structure of sharp constants and extremal sequences for those problems.}, archivePrefix = {arXiv}, author = {Vasyunin, Vasily and Volber, Alexander}, citeulike-article-id = {2565757}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.2247}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.2247}, eprint = {0803.2247}, keywords = {bellman, monge-ampere, stochastic-control}, month = {Mar}, posted-at = {2008-03-20 10:33:32}, priority = {2}, title = {Monge\&\#45;\&\#45;Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems}, url = {http://arxiv.org/abs/0803.2247}, year = {2008} }

TY - ELEC ID - citeulike:2565757 L3 - citeulike-article-id:2565757 N2 - Monge--Amp\`ere equation plays an important part in Analysis. For example, it is instrumental in mass transport problems. On the other hand, the Bellman function technique appeared recently as a way to consider certain Harmonic Analysis problems as the problems of Stochastic Optimal Control. This brings us to Bellman PDE, which in stochastic setting is often a Monge--Amp\`ere equation or its close relative. We explore the way of solving Monge--Amp\`ere equation by a sort of method of characteristics to find the Bellman function of certain classical Harmonic Analysis problems, and, therefore, of finding full structure of sharp constants and extremal sequences for those problems. TI - Monge--Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems KW - bellman KW - monge-ampere KW - stochastic-control AU - Vasyunin, Vasily AU - Volber, Alexander PY - 2008/Mar/14/ UR - http://arxiv.org/abs/0803.2247 ER -