Irregular obstacles and quasi-variational inequalities of stochastic impulse control

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1. [1] A. Bensoussan - J.L. Lions, Contrôle impulsionnel et contrôle continu. Méthode des I.Q.V. non linéaires, C. R. Acad. Sci. Paris, Série A, 278 (1974), pp. 675-679, 747-751. Zbl0316.49002
2. [2] A. Bensoussan - J.L. Lions, Optimal impulse and continuous control: Method of non linear quasi-variational inequalities, Trudy Mat. Inst. Steklov, 134 (1975), pp. 5-22. Zbl0324.49005MR405197
3. [3] A. Bensoussan - J.L. Lions, Sur le controle impulsionnel et les inéquations quasi-variationnelles d'evolution, C. R. Acad. Sci. Paris, Série A, 280 (1975), pp. 1049-1053. Zbl0305.49008MR371469
4. [4] A. Bensoussan - J. Frehse - U. Mosco, A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality, J. Reine Angew. Math., to appear. Zbl0474.49013
5. [5] M. Biroli, A De Giorgi-Nash-Moser result for variational inequalities, Boll. Un. Mat. Ital. (5) 16-A (1979), pp. 598-605. Zbl0424.35035MR551388
6. [6] M. Biroli, An estimate on convergence of approximation by iterations of a solution to a quasi variational inequality and some consequences on continuous dependence and G-convergence, Ann. Mat. Pura Appl., to appear. Zbl0445.49010MR565064
7. [7] L. Caffarelli - A. Friedman, Regularity of the solution of the Q.V.I. for the impulse control problem, Comm. Partial Diff. Eq., 3 (1978), pp. 745-753. Idem II, ibidem. Zbl0385.35010MR499353
8. [8] J. Frehse, On the smoothness of solutions of variational inequalities with obstacles, Proc. Semester Partial Diff. Eq., Banach Center, Warszawa1978. Zbl0568.35009
9. [9] J. Frehse, On Signorini's problem and variational problems with thin obstacles, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 343-362. Zbl0353.49020MR509085
10. [10] J. Frehse, On the regularity of solutions to elliptic differential inequalities, J. Reine Angew. Math., to appear. Zbl0482.35018MR657387
11. [11] J. Frehse - U. Mosco, Sur la régularité de certaines inéquations variationnelles et quasi -variationnelles, C. R. Acad. Sci. Paris, Série A, 289 (1979), pp. 627-630. Zbl0398.49006MR531243
12. [12] J. Frehse - U. Mosco, Variational inequalities with onesided irregular obstacles, Manuscripta Math., 28 (1979), pp. 219-233. Zbl0447.49006MR535703
13. [13] M.G. Garroni - G.M. Troianiello, Some regularity results and a priori estimates for solutions of variational and quasi-variational inequalities, Proc. Conf. Recent methods in nonlinear analysis and Applications, Roma1978, edited by E. DE GIORGI, E. MAGENES and U. Mosco, Pitagora Ed., Bologna, 1979. Zbl0408.35003MR533184
14. [14] B. Hanouzet - J.L. Joly, Méthodes d'ordre dans l'interpretation de certaines inéquations variationnelles, C. R. Acad. Sci. Paris, Série A, 281 (1975), pp. 373-376. Zbl0322.49010MR382838
15. [15] B. Hanouzet - J.L. Joly, Convergence uniforme des iterées définissant la solution d'une inequation quasi-variationnelle, C. R. Acad. Sci. Paris, Série A, 286 (1978), pp. 735-738. Zbl0373.49012MR496035
16. [16] S. Hildebrandt - K.O. Widman, Some regularity results for quasi-linear elliptic systems of second order, Math. Z., 142 (1975), pp. 67-86. Zbl0317.35040MR377273
17. [17] S. Hildebrandt - K.O. Widman, On the Hölder continuity of Weak Solutions of quasi-linear elliptic systems of second order, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 145-178. Zbl0353.35013MR457936
18. [18] J.L. Joly - U. Mosco, A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnelles, J. Functional Analysis, 34 (1979), pp. 107-197. Zbl0425.49018MR551113
19. [19] J.L. Joly - U. Mosco - G.M. Troianiello, On the regular solution of a quasi variational inequality connected to a problem of stochastic impulse control, J. Math. Anal. Appl., 61 (1977), pp. 357-369. Zbl0403.49014MR493585
20. [20] Ky Fan, A minimax inequality and applications, in Inequalities III, Shisha ed., Academic Press, New York, 1972, pp. 103-113. Zbl0302.49019MR341029
21. [21] O.A. Ladyzhenskaia - N. Ural'tseva, Linear and quasi-linear elliptic equations, Acad. Press, New York, 1979. 
22. [22] H. Lewy - G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), pp. 153-188. Zbl0167.11501MR247551
23. [23] H. Lewy - G. Stampacchia, On the smoothness of superharmonies which solve a minimum problem, J. Analyse Math., 23 (1970), pp. 227-236. Zbl0206.40702MR271383
24. [24] J.L. Lions - G. Stampacchia, Variational inequatities, Comm. Pure Appl. Math., 20 (1967), pp. 493-519. Zbl0152.34601MR216344
25. [25] J.L. Menaldi, Sur le problème de contrôle impulsionnel et l'inéquation quasi variationnelle degenerée associée, C. R. Acad. Sci. Paris, Série A, 284 (1977), pp. 1499-1502. Zbl0363.49002MR441526
26. [26] U. Mosco - G.M. Troianiello, On the smoothness of solutions of unilateral Dirichlet problems, Boll. Un. Mat. Ital., 8 (1973), pp. 57-67. Zbl0277.35033MR390479
27. [27] U. Mosco, Implicit variational problems and quasi variational inequalities, in Nonlinear operators and calculus of variations, Proc. Bruxelles, 1975, edited by L. WAELBROECK, Lecture Notes in Math., 543, Springer-Verlag, 1976. Zbl0346.49003MR513202
28. [28] U. Mosco, Nonlinear quasi-variational inequalities and stochastic impulse control theory, Proc. Conf. Equadiff IV, Praha, 1977, edited by J. FÁBERA, Lecture Notes in Math., 703, Springer-Verlag, 1979. Zbl0428.49004MR535348
29. [29] U. Mosco, On some nonlinear quasi variational inequatities and implicit complementarity problems in stochastic control theory, in Variational Inequalities, Proc., edited by R. W. COTTLE, F. GIANNESSI and J. L. LIONS, J. Wiley, 1979. Zbl0486.49004
30. [30] G. Stampacchia, Formes bilinéaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris, Série A, 258 (1964), pp. 4413-4416. Zbl0124.06401MR166591
31. [31] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Grenoble, 15 (1965), pp. 189-258. Zbl0151.15401MR192177
32. [32] F. Tomi, Variationsprobleme vom Dirichlet-type mit einer Ungteichung als Nebenbedingung, Math. Z., 128 (1972), pp. 43-74. Zbl0243.49023MR322624
33. [33] K.O. Widman, Hölder continuity of solutions of elliptic systems, Manuscripta Math., 5 (1971), pp. 299-308. Zbl0223.35044MR296484
34. [34] K.O. Widman, The singularity of the Green function for non-uniformly elliptic partial differential equations with discontinuous coefficients, Technical report, Uppsala Univ., 1970. 

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