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


Author: Lawrence C. Evans
Journal: Trans. Amer. Math. Soc. 275 (1983), 245-255
MSC: Primary 35J60; Secondary 49C20, 93E20
DOI: https://doi.org/10.1090/S0002-9947-1983-0678347-8
MathSciNet review: 678347
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0678347-8
Keywords: Nonlinear elliptic p.d.e, a priori estimate, dynamic programming
Article copyright: © Copyright 1983 American Mathematical Society

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