Variational inequalities of elliptic and parabolic type

Taiwanese Journal of Mathematics

Volumn 6, Issue 3, 2002, Pages 287-322

  Rudd, Matthew ^a   Schmitt, Klaus ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Elliptic variational inequalities; Obstacle problems; Parabolic variational inequalities; Penalty method; Rothe's method; Translation method; Variational inequalities

Indexed keywords

EID: 0038889933     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500558298     Document Type: Article

References (41)

1. R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. G. Aronsson, L. C. Evans, and Y. Wu, Fast/slow diffusion and growing sandpiles, J. Differential Equations, 131 (1996), 304-335.
3. C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities: Applications to Free Boundary Problems, Wiley, New York, 1984.
4. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste România, Bucharest, 1976. Translated from the Romanian.
5. . H. Brézis, Problèmes unilatéraux, J. Math. Pures Appl. (9), 51 (1972), 1-168.
6. H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam, 1973.
7. H. Brézis, Analyse fonctionnelle: théorie et applications, Masson, Paris, 1983.
8. T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998.
9. M. Chipot, Variational Inequalities and Flow in Porous Media, vol. 52 of Applied Math. Sciences, Springer, New York, 1984.
10. P. Clément, M. Garcia-Huidobro, R. Manásevich, and K. Schmitt, Mountain pass type solutions for quasilinear elliptic equations, Calc. Variations and PDE, 11 (2000), 33-62.
11. E. DiBenedetto, Degenerate Parabolic Equations, Springer, Berlin, 1993.
12. N. Dinculeanu, Vector Measures, Pergamon Press, Oxford, 1967.
13. T. Donaldson, Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Differential Equations, 10 (1971), 507-528.
14. G. Duvaut and J. L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972.
15. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North Holland, American Elsevier, New York, 1976.
16. L. C. Evans, M. Feldman, and F. Gariepy, Fast/slow diffusion and collapsing sandpiles, J. Differential Equations, 137 (1997), 166-209.
17. A. Friedman, Variational Principles and Free Boundary Value Problems, Wiley-Interscience, New York, 1983.
18. M. Garcia-Huidobro, V. Le, R. Manásevich, and K. Schmitt, On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting, Nonl. Differential Equations and Applications, 6 (1999), 207-225.
19. J. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) growing coefficients, Trans. Amer. Math. Soc. 190 (1974), 163-205.
20. _, A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces, Proc. Symp. Pure Mathematics, Amer. Math. Soc. 45 (1986), 455-462.
21. E. Hille and R. Phillips, Functional Analysis and Semigroups, AMS Colloquium Publ. vol. 31. 3rd ed., Providence, 1968.
22. J. Kačur, Method of Rothe in Evolution Equations, Teubner Verlagsgesellschaft, Leipzig, 1985.
23. N. Kikuchi and J. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988.
24. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities, Acad. Press, New York, 1980.
25. M. A. Krasnosel'skii and Y. B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
26. A. Kufner, O. John, and S. Fučik, Function Spaces, Noordhoff, Leyden, 1977.
27. V. Le and K. Schmitt, Quasilinear elliptic equations and inequalities with rapidly growing coefficients, J. London Math. Soc. 62 (2000), 852-872.
28. V. K. Le and K. Schmitt, Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems, Springer-Verlag, New York, 1997.
29. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
30. F. Mignot and J.-P. Puel, Inéquations variationelles et quasivariotionelles hyperboliques du premier ordre, J. Math. Pures Appl. 55 (1976), 353-378.
31. H. Nagase, On an application of Rothe's method to nonlinear parabolic variational inequalities, Funkcial. Ekvac. 32 (1989), 273-299.
32. D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Sijthoff and Noordhoff, Bucharest, 1978.
33. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
34. M. Rao and Z. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1985.
35. T. R. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
36. J. Rodrigues and L. Santos, A parabolic quasi-variational inequality arising in a superconductivity model, Ann. Scuola Norm. Pisa Cl. Sci. 29 (2000), 153-169.
37. J. F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland, Amsterdam, 1987.
38. R. E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman, London, 1977.
39. _, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Math. Soc., Providence, 1997.
40. E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol.3: Variational Methods and Optimization, Springer, Berlin, 1985.
41. A. Ženíšek, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations, Academic Press Inc., London, 1990.