Some asymptotic problems in fully nonlinear elliptic equations and stochastic control

 Access to full text

 Full (PDF)

1. [1] H. Amann - M.G. Crandall, On some existence theorems for semilinear elliptic equations, Ind. Univ. Math. J., Zbl0391.35030
2. [2] A. Bensoussan, Homogenization theory, Conferenze del seminario di matematica dell'Università di Bari, 158 (1979). Zbl0431.35009MR568125
3. [3] A. Bensoussan - J.L. Lions - G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland (1978), Amsterdam. Zbl0404.35001MR503330
4. [4] A. Bensoussan - P.L. Lions, Optimal control of random evolutions, Stochastics, 5 (1981), pp. 169-199. Zbl0472.93073MR631995
5. [5] J.M. Bony, Principe du maximum dans les espaces de Sobolev, Comptes-Rendus Paris, 265 (1967), pp. 333-336. Zbl0164.16803MR223711
6. [6] H. Brèzis, Opèrateurs maximaux monotones, North-Hollans (1973). 
7. [7] H. Brèzis - L.C. Evans, A variational approach to the Bellman-Dirichlet equation for two elliptic operators, Arch. Rat. Mech. Anal., 71 (1979), pp. 1-14. Zbl0447.49022MR522704
8. [8] Cafflish - P.L. Lions, to appear. Zbl1157.01313
9. [9] J.P. Chow - P.V. Kokotovic, Decomposition of near optimal state regulation for systems with slow and fast modes, IEEE, Tr. Autom. Control (1976). Zbl0332.49034
10. [10] P. Ciarlet, A justification of the Von Kármán equations, Arch. Rat. Mech Anal., 75 (1980), pp. 349-389. Zbl0443.73034MR569597
11. [11] P. Ciarlet - P. Destuynder, A justification of the two-dimensional linear plate model, J. Mécanique, 18 (1979), pp. 315-344. Zbl0415.73072MR533827
12. [12] P. Ciarlet - P. Destuynder, A justification of a nonlinear model in plate theory, Comput. Methods Appl. Mech. Engreg., 17/18 (1979), pp. 227-258. Zbl0405.73050MR533827
13. [13] P. Ciarlet - P. Rabier, Ler équations de Von Kármán, Lecture Notes in Mathematics, no. 826, Springer, Berlin, 1980. Zbl0433.73019MR595326
14. [14] E. De Giorgi - S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellitici del secondo ordine, Boll. Un. Mat. Ital., 8 (1973), pp. 391-411. Zbl0274.35002MR348255
15. [15] L.C. Evans, A convergence theorem for solutions of nonlinear elliptic equations, Ind. Univ. Math. J., 27 (1978), pp. 875-887. Zbl0408.35037MR503721
16. [16] L.C. Evans, On solving certain nonlinear partial differential equations by accretive operator methods, Isr. J. Math., 36 (1980), pp. 225-247. Zbl0454.35038MR597451
17. [17] L.C. Evans, Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math. Math., 1982. Zbl0469.35022MR649348
18. [18] L.C. Evans - A. Friedman, Optimal stochastic switching and the Dirichlet problem for the Bellman equation, Trans. Amer. Math. Soc., 253 (1979), pp. 365-389. Zbl0425.35046MR536953
19. [19] L.C. Evans - P.L. Lions, Résolution des équations de Hamilton-Jacobi-Bellman pour des opèrateurs uniformement e.liptiques, Comptes-Rendus Paris, 290 (1980), pp. 1049-1052. Zbl0461.49017MR582494
20. [20] L.C. Evans - P.L. Lions, Fully nonlinear second order elliptic equations with large zeroth order coefficient, Ann. Inst. Fourier, 31 (1981), pp. 175-191. Zbl0441.35023MR617246
21. [21] W.H. Fleming - R. Rishel, Deterministic and stochastic optimal control, Springer, Berlin, 1975 Zbl0323.49001MR454768
22. [22] C. Foias - P.L. Lions, to appear. 
23. [23] N.V. Krylov, Controlled diffusion processes, Springer, Berlin, 1980. Zbl0459.93002MR601776
24. [24] W.A. Ladyzhenskaja - N.N. Uralt'seva, Linear and quasilinear elliptic equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
25. [25] P.L. Lions, Résolution analytique des problèmes de Bellman-Dirichlet, Acta Mathematica, 146 (1981), pp. 151-166; See also Comptes-Rendus Paris, 287 (1978), pp. 747-750. Zbl0467.49016MR611381
26. [26] P.L. Lions, Control of diffusion processes in RN, Comm. Pure Appl. Math., 34 (1981), pp. 121-147; See also Comptes-Rendus Paris, 288 (1979), pp. 339-342. Zbl0441.49020MR600574
27. [27] P.L. Lions, Equations de Hamilton-Jacobi-Bellman dégénérées, Comptes-Rendus Paris, 289 (1979), pp. 329-332. Zbl0424.49014MR552287
28. [28] P.L. Lions, Résolution de problèmes quasilineaires, Arch. Rat. Mech. Anal., 74 (1980), pp. 335-354. Zbl0449.35036MR588033
29. [29] P.L. Lions, Problèmes elliptiques du deuxième ordre non sour forme divergence, Proc. Roy. Soc. Edinburgh, 84A (1979), pp. 263-271. Zbl0422.35033MR559671
30. [30] P.L. Lions, Some problems related to the Bellman-Dirichlet equation for two operators, Comm. in Partial Diff. Equations, 5 (7) (1980), pp. 753-771. Zbl0435.35035MR579996
31. [31] P.L. Lions, A remark on some elliptic second-order problems, Boll. Un. Mat. Ital., 17 (1980), pp. 267-270. Zbl0428.35039MR578358
32. [32] P.L. Lions, Equations de Hamitton-Jacobi-Bettman, In «Seminaire Goulaouic-Schwartz 1979-80 », Ecole Polytechnique, Paris, 1981. Zbl0452.35007
33. [33] P.L. Lions, Une inégalité pour les opérateurs elliptiques du second ordre, Ann. Mat. Pura Appl., 77 (1981), pp. 1-11. Zbl0468.35040MR633391
34. [34] P.L. Lions, Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman, Ann. de Toulouse, 3 (1981), pp. 59-68. Zbl0467.49017MR624131
35. [35] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Comm. P.D.E., 8 (1983), pp. 1101-1174, pp. 1229-1276 and in Nonlinear PDE and applications, vol. V, Pitman, London, 1983. Zbl0716.49022
36. [36] R.E. O'Malley, The singular perturbed linear state regulator, S.I.A.M. J. Control, 13 (1975). 
37. [37] C. Pucci, Limitazioni per soluzioni di equazioni ellitiche, Ann. Mat. Pura Appl., 74 (1966), pp. 15-30. Zbl0144.35801MR214905
38. [38] M.V. Safonov, On the Dirichlet problem for the Bellman equation in a bounded domain, Dokl. Akad. Nauk. U.S.S.R., (1980), pp. 535-540 (in Russian). Zbl0481.93065MR581407
39. [39] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent oariables, Phil. Trans. Roy. Soc. London, 264 (1969), pp. 413-496. Zbl0181.38003MR282058

1. Italo Capuzzo Dolcetta, Soluzioni di viscosità