This article is cited in 19 papers

Smoothness of the value function for a controlled diffusion process in a domain

N. V. Krylov


Abstract: The author gives conditions on the behavior of a controlled diffusion process within and on the boundary of a domain that are sufficient for the value function to have two bounded generalized derivatives and to satisfy the Bellman equation. These conditions are almost necessary even for uncontrolled diffusion processes, and at the same time they encompass, for example, the heat equation in a disc and the Monge-Ampère equation in a convex domain.
Bibliography: 24 titles.

UDC: 517.9

MSC: Primary 60J60, 58G32, 35J25; Secondary 35K20, 60H10

Received: 01.07.1987

 English version: Mathematics of the USSR-Izvestiya, 1990, 34:1, 65–95

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