On The Dirichlet Problem for Bellman’s Equation in A Plane Domain

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Abstract

The Dirichlet problem for Bellman’s equation in a plane domain is considered. It is shown that, under certain assumptions about the type of smoothness and the “weak” nondegeneracy of the corresponding controlled diffusion process, the solution of this Dirichlet problem is the pay-off function of an optimal control problem. Under supplementary assumptions about smoothness, the pay-off function is also smooth.

Original languageEnglish (US)
Pages (from-to)231-248
Number of pages18
JournalMathematics of the USSR - Sbornik
Volume31
Issue number2
DOIs
StatePublished - Feb 28 1977

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