Monge--Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems
By V. Vasyunin, Alexander Volberg. 2008
92 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/94136005fe59d8ceeeadf3bae17edb8584bfd23d
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Sharp L^p estimates on BMO (2011, background): “Those works, together with [VV2], initiated the study of the relationship among explicit Bellman functions, the Monge–Ampère geometry of Bellman domains, and the structure of optimizers in the corresponding inequalities.”