2008/03/14 by Vasily Vasyunin, Alexander Volberg, Vasyunin, Vasily +1 · 1 citation
Mathematics · #28A75 #28A80 #60D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #msc:28A75 #msc:28A80 #msc:60D05
paper · pdf · doi:10.48550/arxiv.0803.2247
openalex publication_date 2008/03/14 · arxiv created 2008/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Monge--Ampère 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--Ampère equation or its close relative. We explore the way of solving Monge--Ampère 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.