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Evans, Lawrence C.; Friedman, Avner

Optimal stochastic switching and the Dirichlet problem for the Bellman equation. (English) Zbl 0425.35046

Trans. Am. Math. Soc. 253, 365-389 (1979).
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Cited in 1 Review
Cited in 62 Documents

MSC:

35J60 Nonlinear elliptic equations
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities
35J25 Boundary value problems for second-order elliptic equations
47H05 Monotone operators and generalizations
47J05 Equations involving nonlinear operators (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control

Keywords:

optimal stochastic switching; Bellman equation; second order elliptic operators; nonlinear elliptic equations
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\textit{L. C. Evans} and \textit{A. Friedman}, Trans. Am. Math. Soc. 253, 365--389 (1979; Zbl 0425.35046)
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References:

[1] Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. · Zbl 0328.47035
[2] Alain Bensoussan and Jacques-Louis Lions, Contrôle impulsionnel et systèmes d’inéquations quasi variationnelles, C. R. Acad. Sci. Paris Sér. A 278 (1974), 747 – 751 (French). · Zbl 0316.49003
[3] A. Bensoussan and J.-L. Lions, Applications des inéquations variationnelles en contrôle stochastique, Dunod, Paris, 1978 (French). Méthodes Mathématiques de l’Informatique, No. 6. · Zbl 0411.49002
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[8] Maurizio Chicco, Principio di massimo per soluzioni di equazioni ellittiche del secondo ordine di tipo Cordes, Ann. Mat. Pura Appl. (4) 100 (1974), 239 – 258 (Italian, with English summary). · Zbl 0289.35071 · doi:10.1007/BF02412159
[9] Lawrence C. Evans, A convergence theorem for solutions of nonlinear second-order elliptic equations, Indiana Univ. Math. J. 27 (1978), no. 5, 875 – 887. · Zbl 0408.35037 · doi:10.1512/iumj.1978.27.27059
[10] Lawrence C. Evans and Pierre-Louis Lions, Deux résultats de régularité pour le problème de Bellman-Dirichlet, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 13, A587 – A589 (French, with English summary). · Zbl 0371.35013
[11] Avner Friedman, Stochastic differential equations and applications. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Probability and Mathematical Statistics, Vol. 28. Avner Friedman, Stochastic differential equations and applications. Vol. 2, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Probability and Mathematical Statistics, Vol. 28. · Zbl 0323.60056
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