Brézis, Haïm; Evans, L. C. A variational inequality approach to the Bellman-Dirichlet equation for two elliptic operators. (English) Zbl 0447.49022 Arch. Ration. Mech. Anal. 71, 1-13 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 25 Documents 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) Keywords:Bellman-Dirichlet equation PDFBibTeX XMLCite \textit{H. Brézis} and \textit{L. C. Evans}, Arch. Ration. Mech. Anal. 71, 1--13 (1979; Zbl 0447.49022) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.