Geodesic
On some Variational Inequalities in Unbounded Domains
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 243-262.

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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. 
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     title = {On some {Variational} {Inequalities} in {Unbounded} {Domains}},
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Chipot, Michel; Yeressian, Karen. On some Variational Inequalities in Unbounded Domains. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 243-262. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a4/

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