Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators

Evans, Lawrence C.

doi:10.1090/S0002-9947-1983-0678347-8

Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators
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Trans. Amer. Math. Soc. 275 (1983), 245-255 Request permission

Abstract:

We prove under appropriate hypotheses that the Hamilton-JacobiBellman dynamic programming equation with uniformly elliptic operators, ${\max _{1 \leqslant k \leqslant m}}\{{L^k}u - {f^k}\} = 0$, has a classical solution $u \in {C^{2,\beta }}$, for some (small) Hölder exponent $\beta > 0$.

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