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A capacitary method for the asymptotic analysis of dirichlet problems for monotone operators

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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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Authors and Affiliations

  1. SISSA, Via Beirut 4, 34013, Trieste, Italy

    Gianni Dal Maso

  2. Dipartimento di Matematica, Università “La Sapienza”, Piazzale A.Moro 5, 00185, Roma, Italy

    Adriana Garroni

  3. Institute of Applied Mathematics and Mechanics, Academy of Sciences of Ukraine, R. Luxemburg St. 74, 340114, Donetsk, Ukraine

    Igor V. Skrypnik

Authors
  1. Gianni Dal Maso
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  2. Adriana Garroni
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  3. Igor V. Skrypnik
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Correspondence to Gianni Dal Maso.

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Dal Maso, G., Garroni, A. & Skrypnik, I.V. A capacitary method for the asymptotic analysis of dirichlet problems for monotone operators. J. Anal. Math. 71, 263–313 (1997). https://doi.org/10.1007/BF02788033

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  • DOI: https://doi.org/10.1007/BF02788033

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