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Selected Works of Alexander M. Stokolos
Article
Monge-Ampère Equations and Bellman Functions: The Dyadic Maximal Operator
Comptes Rendus Mathematique (2008)
  • Leonid Slavin, University of Missouri
  • Alexander M. Stokolos, Georgia Southern University
  • Vasily Vasyunin, Russian Academy of Sciences
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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.
Keywords
  • Monge--Ampère equations,
  • Bellman functions
Disciplines
Publication Date
May, 2008
DOI
10.1016/j.crma.2008.03.003
Citation Information
Leonid Slavin, Alexander M. Stokolos and Vasily Vasyunin. "Monge-Ampère Equations and Bellman Functions: The Dyadic Maximal Operator" Comptes Rendus Mathematique Vol. 346 Iss. 9-10 (2008) p. 585 - 588 ISSN: 1631-073X
Available at: http://works.bepress.com/alex_stokolos/5/