Monge-Ampère equations and Bellman functions: The dyadic maximal operator

Leonid Slavin, Alexander Stokolos, Vasily Vasyunin

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We find explicitly the Bellman function for the dyadic maximal operator on Lp as the solution of a Bellman partial differential equation of Monge-Ampère type. This function has been previously found by A. Melas (2005) in a different way, but it is our partial differential equation-based approach that is of principal interest here. Clear and replicable, it holds promise as a unifying template for past and current Bellman function investigations. To cite this article: L. Slavin et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original languageEnglish
Pages (from-to)585-588
Number of pages4
JournalComptes Rendus Mathematique
Volume346
Issue number9-10
DOIs
StatePublished - May 2008

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