Abstract
We are concerned with the d-dimensional Bellman equation of the form:
where
and │·│, (,), and D denote the norm, the inner product of vectors, and the gradient respectively. We are given a convex function h(x) with polynomial growth, and the unknown is the pair of a constant λ and a C 2-function φ(x) on R d.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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References
Agmon, S., Douglis, A. and Nirenberg, L. (1959). Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12: 623 - 727.
Bensoussan, A. (1982). Stochastic Control by Functional Analysis Methods. North-Holland, Amsterdam.
Bensoussan, A. and Frehse, J. (1992). On Bellman equations of ergodic control in R. J. reine angew. Math. 429: 125 - 160.
Brezis, H. (1992). Analyse Fonctionnelle;Théorie et applications. Masson, Paris.
Gilbarg, D. and Trudinger, N.S. (1983) Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
Morimoto, H. and Okada, M. Some results on Bellman equation of ergodic control. SIAM J. Control Optim. to appear.
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© 1999 IFIP International Federation for Information Processing
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Morimoto, H., Fujita, Y. (1999). Radial Symmetry of Classical Solutions for Bellman Equations in Ergodic Control. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_31
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DOI: https://doi.org/10.1007/978-0-387-35359-3_31
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