On some Variational Inequalities in Unbounded Domains
Chipot, Michel ; Yeressian, Karen
Bollettino dell'Unione Matematica Italiana, Tome 5 (2012), p. 243-262 / Harvested from Biblioteca Digitale Italiana di Matematica
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We study the variational formulation of the obstacle problem in unbounded domains when the force term might grow at infinity. We derive the appropriate variational formulation and prove existence and uniqueness of solution. We also show the rate of growth at infinity of the solution in terms of the growth rates of the obstacle and the force, and prove the exponential convergence of the solutions in approximating bounded domains to the solution in the unbounded domain.

Publié le : 2012-06-01
@article{BUMI_2012_9_5_2_243_0,
     author = {Michel Chipot and Karen Yeressian},
     title = {On some Variational Inequalities in Unbounded Domains},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5},
     year = {2012},
     pages = {243-262},
     zbl = {1258.49005},
     mrnumber = {2977248},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_2_243_0}
}

Chipot, Michel; Yeressian, Karen. On some Variational Inequalities in Unbounded Domains. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 243-262. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_2_243_0/

[C0] Chipot, M., ℓ goes to plus infinity, Birkäuser, 2002. | MR 1999898 | Zbl 1129.35014

[C1] Chipot, M., Variational inequalities and flows in porous media, Springer, Berlin, 1984. | MR 747637 | Zbl 0544.76095

[C2] Chipot, M., Elements of nonlinear analysis, Birkäuser, 2000. | MR 1801735 | Zbl 0964.35002

[CM] Chipot, M. - Mardare, S., To appear.

[CY] Chipot, M. - Yeressian, K., Exponential rates of convergence by an iteration technique, C. R. Acad. Sci. Paris Ser. I, 346 (2008), 21-26. | MR 2383116 | Zbl 1134.35016

[DL] Dautray, R. - Lions, J. L., Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1990. | MR 1036731 | Zbl 0683.35001

[KS] Kinderlehrer, D. - Stampacchia, G., An introduction to variational inequalities and their applications, Academic Press, New York, 1980. | MR 567696 | Zbl 0457.35001

[LS] Lions, J. L. - Stampacchia, G., Variational inequalities, Comm. Pure Applied Math, 20 (1967), 493-519. | MR 216344

[R] Rodrigues, J. F., Obstacle problems in mathematical physics, Mathematical Studies134, North-Holland, 1987. | MR 880369 | Zbl 0606.73017

[Y] Yeressian, K., Spatial Asymptotic Behavior of Elliptic Equations and Variational Inequalities, Thesis, University of Zurich, 2010.