A Variational Inequality Approach to the Bellman-Dirichlet Equation for Two Elliptic Operators
نویسندگان
چکیده
We prove existence, uniqueness, and regularity properties for a solution u of the Bellman-Dirichlet equation of dynamic programming: (1) max {I]u+f i} =0 in (2 i = 1 , 2 u=O on 092, where D and L 2 are two second order, uniformly elliptic operators. The method of proof is to rephrase (1) as a variational inequality for the operator K = L 2 (D)1 in L2(O) and to invoke known existence theorems. For sufficiently nice f l and f2 we prove in addition that u is in H a (f2)c~ C2'~(O) (for some 0 < c~ < 1) and hence is a classical solution of (1).
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