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A variational inequality approach to the Bellman-Dirichlet equation for two elliptic operators. (English) Zbl 0447.49022

MSC:
49L20 Dynamic programming in optimal control and differential games
49J40 Variational inequalities
35J25 Boundary value problems for second-order elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
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[1] H. Brezis, Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, Math. Studies 5, North Holland, 1973.
[2] H. Brezis & D. Kinderlehrer, The smoothness of solutions of nonlinear variational inequalities, Indiana U. Math. J. 23 (1974), 831–844. · Zbl 0278.49011 · doi:10.1512/iumj.1974.23.23069
[3] W. H. Fleming & R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, New York 1975. · Zbl 0323.49001
[4] N. V. Krylov, Control of a solution of a stochastic integral equation, Theory Prob. and Appl. 17 (1972), 114–131. · Zbl 0265.60055 · doi:10.1137/1117009
[5] H. J. Kushner, Stochastic Stability and Control, Academic Press, New York, 1967. · Zbl 0244.93065
[6] O. A. Lady<zenskaja, On integral inequalities, the convergence of approximative methods, and the solution in functional for linear elliptic operators, Vestnik, Leningrad State University 7 (1958), 60–69 (Russian).
[7] O. A. Lady<zenskaja & N. N. Ural’ceva, Linear Quasilinear Elliptic Equations, Academic Press, New York, 1968.
[8] M. Nisio, Remarks on stochastic optimal controls, Japan J. Math. 1 (1975), 159–183. · Zbl 0334.93054
[9] C. Pucci, Operatori ellittici estremanti, Ann. Mat. Pura. Appl. 72 (1966), 141–170. · Zbl 0154.12402 · doi:10.1007/BF02414332
[10] J. Serrin, Local behavior of solutions of quasi-linear elliptic equations. Acta Math. 111 (1964), 247–302. · Zbl 0128.09101 · doi:10.1007/BF02391014
[11] P. Sobolevsky, Equations with operators constituting an acute angle, Doklady. Akad. Nauk. USSR 11b (1957), 754–757 (Russian). · Zbl 0081.11802
[12] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, University of Montreal Press, 1966. · Zbl 0151.15501
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