TY - JOUR
T1 - Monge-Ampère equations and Bellman functions
T2 - The dyadic maximal operator
AU - Slavin, Leonid
AU - Stokolos, Alexander
AU - Vasyunin, Vasily
PY - 2008/5
Y1 - 2008/5
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=42649083996&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2008.03.003
DO - 10.1016/j.crma.2008.03.003
M3 - Article
SN - 1631-073X
VL - 346
SP - 585
EP - 588
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 9-10
ER -