A capacitary method for the asymptotic analysis of dirichlet problems for monotone operators |
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| Authors: | Gianni Dal Maso Adriana Garroni Igor V Skrypnik |
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| Institution: | (1) SISSA, Via Beirut 4, 34013 Trieste, Italy;(2) Dipartimento di Matematica, Università “La Sapienza”, Piazzale A.Moro 5, 00185 Roma, Italy;(3) Institute of Applied Mathematics and Mechanics, Academy of Sciences of Ukraine, R. Luxemburg St. 74, 340114 Donetsk, Ukraine |
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| Abstract: | Given a non-linear elliptic equation of monotone type in a bounded open set Ω ⊂ Rn, we prove that the asymptotic behaviour, asj → ∞, of the solutions of the Dirichlet problems corresponding to a sequence (Ωj) of open sets contained in Ω is uniquely determined by the asymptotic behaviour, asj → ∞, of suitable non-linear capacities of the setsKΩ
j, whereK runs in the family of all compact subsets of Ω. |
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