An order approach to a class of quasivariational sweeping processes

Advances in Differential Equations

Volumn 10, Issue 5, 2005, Pages 527-552

  Rossi, Riccarda ^a   Stefanelli, Ulisse ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b CNR   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645429681     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. F. Auricchio and U. Stefanelli, Numerical analysis of a 3-D super-elastic constitutive model, Int. J. Numerical Meth. Engineering, to appear, 2004.
2. F. Auricchio and U. Stefanelli, Well-posedness and approximation for a onedimensional model for shape memory alloys, Submitted, 2004.
3. P. Ballard, A counter-example to uniqueness in quasi-static elastic contact problems with friction, Internat. J. Engrg. Sci., 37 (1999), 163-178.
4. C. Baiocchi and A. Capelo, "Variational and Quasivariational Inequalities, Applications to Free Boundary Problems," John Wiley & Sons Inc., New York, 1984.
5. A. Bensoussan, M. Goursat, and J.-L Lions, Contrôle impulsionnel et inéquations quasi-variationnelles stationnaires, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), A1279-A1284.
6. H. Brezis, "Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert," North Holland Math. Studies, 5. North Holland, Amsterdam, 1973.
7. H. Brezis and G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques, Bullettin de la S.M.F., 96 (1968), 153-180.
8. M. Brokate, P. Krejčí, and H. Schnabel, On uniqueness in evolution quasivariational inequalities, Preprint, 2002.
9. M. Chraibi Kaadoud, Résolution de problèmes de rafle et application à un problème de frottement, Topol. Methods Nonlinear Anal., 18 (2001), 1:89-102.
10. I.I. Kolodner, On completeness of partially ordered sets and fixpoint theorems for isotone mappings, Amer. Math. Monthly, 75 (1968), 48-49.
11. M. Kunze and M.D.P. Monteiro Marques, On parabolic quasi-variational inequalities and state-dependent sweeping processes, Topol. Methods Nonlinear Anal., 12 (1998), 179-191.
12. M. Kunze and M D.P. Monteiro Marques, An introduction to Moreau's sweeping process, In "Impacts in mechanical systems (Grenoble 1999)," Lecture Notes in Phys., 551, pages 1-60. Springer, Berlin, 2000.
13. F. Mignot and J.-P. Puel, Inéquations d'évolution paraboliques avec convexes dépendant du temps, Applications aux inéquations quasi variationnelles d'évolution, Arch. Rational Mech. Anal., 64 (1977), 59-91.
14. M.D.P. Monteiro Marques, "Differential Inclusions in Nonsmooth Mechanical Problems-Shocks and Dry Friction," Birkhaüser, Basel Boston Berlin 1993.
15. J.-J. Moreau, Sur les mesures différentielles de fonctions vectorielles, Séminaire d'analyse convexe, Montpellier, 4, exposé n. 15, 1975.
16. J.-J. Moreau, Sur les mesures différentielles de fonctions vectorielles et certains problèmes d'évolution, C. R. Acad. Sci. Paris, Sér. A-B, 282 (1976), 837-840.
17. J.-J. Moreau, Problème d'évolution associé à un convexe mobile d'un espace hilbertien, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), A791-A794.
18. J.-J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Equations, 26 (1977), 347-374.
19. R.T. Rockafellar and R.J.-B Wets, "Variational Analysis," Grundlehren der Mathematischen Wissenschaften, vol. 317, Springer-Verlag, Berlin, 1998.
20. L. Simon, Lectures on geometric measure theory, Proceedings of the Center for Mathematical Analysis, 3, Australian National University, Canberra 1983.
21. U. Stefanelli, Nonlocal quasivariational evolution problems, Submitted, 2004.
22. U. Stefanelli, Some quasivariational problems with memory, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 8 (2004), 319-333.
23. L. Tartar, Inéquations quasi variationnelles abstraites, C. R. Acad. Sci. Paris Sér. A, 278 (1974), A1193-A1196.