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References
Amann, H., Crandall, M.G.: On some existence theorems for semilinear elliptic equations. Ind. Univ. Math. J27, 779–790 (1978)
Bensoussan, A., Lions, J.L.: Applications des inéquations variationnelles on contrôle stochastique. Paris: Dunod 1978
Bensoussan, A., Lions, J.L.: Contrôle impulsionnel et inéquations quasi-variationnelles. Paris: Dumod 1982
Bombieri, E., De Giorgi, E., Miranda, M.: Una maggiorazioni a priori relativa alle ipersuperfici minimali non parametriche. Arch. Rat. Mech. Anal.32, 255–267 (1969)
Bony, J.M.: Principe du maximum dans les espaces de Sobolev. Cr. Acad. Sci. Paris265, 233–236 (1967)
Brézis, H.: Semilinear equations in ℝn without condition ar infinity. Appl. Math. Opt.12, 271–282 (1984)
Crandall, M.G., Lions, P.L.: Remarks on unbounded viscosity solutions of Hamilton-Jacobiequations. Ill. J. Math.31, 665–688 (1987)
Fleming, W.H., Rishel, R.: Deterministic and stochastic optimal control. Berlin Heidelberg New York: Springer 1975
Holland, C.J.: A new energy characterization of the smallest eigenvalue of the Schrödinger equation. Comm. Pure Appl. Math.30, 755–765 (1977)
Holland, C.J.: A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions. Comm. Pure Appl. Math.31, 509–519 (1978)
Krylov, N.V.: Controlled diffusion processes. Berlin Heidelberg New York: Springer 1980
Krylov, N.V.: Nonlinear second-order elliptic and parabolic equations. Moscow: Nauk 1985 (in Russian)
Ladyshenskaya, O., Ural'tseva, N.: Local estimates for gradients of solutions of nonuniformly elliptic and parabolic equations. Comm. Pure Appl. Math.23, 677–703 (1970)
Laetsch, T.: On the number of solutions of boundary value problems with convex nonlinearities. J. Math. Anal. Appl.35, 389–404 (1971)
Lasry, J.M., Lions, P.L.: In preparation
Lions, P.L.: Resolution de problèmes elliptiques quasilinéaires. Arch. Rat. Mech. Anat.74, 336–353 (1980)
Lions, P.L.: On the Hamilton-Jacobi-Bellman equations. Acta Applicandae1, 17–41 (1983)
Lions, P.L: Some recent results in the optimal control of diffusion processes. In: Stochastic Analysis, Proceedings in the Taniguchi International Symposium on Stochastic Analysis, Katata, Kyoto (1982). Tokyo: Kinokuniya 1984
Lions, P.L.: Quelques remarques sur les problèmes elliptiques quasillineaires du second ordre. J. Anal. Math.45, 234–254 (1985)
Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations and boundary conditions. Preprint
Lions, P.L.: Generalized solutions of Hamilton-Jacobi equations. London: Pitman 1982
Lions, P.L.: Neumann type boundary conditions for Hamilton-Jacobi equations. Duke Math. J.52, 793–820 (1985)
Lions, P.L.: A remark on Bony maximum principle. Proc. Am. Math. Soc.88, 503–508 (1983)
Lions, P.L., Trudinger, N.S.: Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equations. Math. Z.191, 4–15 (1985)
Lions, P.L., Trudinger, N.S.: In preparation
Simon, L.: Interior gradient bounds for nonuniformly elliptic equations. Ind. Univ. Math. J.25, 821–855 (1976)
Simon, L.: Boundary regularity for solutions of the nonparametric least area problem. Ann. Math.103, 429–455 (1976)
Simon, L.: Global estimates of Hölder continuity for a class of divergence form equations. Arch. Rat. Mech. Anal.56, 223–272 (1974)
Soner, M.H.: Optimal control with state-space constraints. I. SIAM J. Control Optim. (1986)
Urbas, J.I.E.: Elliptic equations of Monge-Ampere type. Thesis, Univ. of Canberra, Australla, 1984
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Lasry, J.M., Lions, P.L. Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. Math. Ann. 283, 583–630 (1989). https://doi.org/10.1007/BF01442856
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DOI: https://doi.org/10.1007/BF01442856