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A property of nonlinear elliptic equations when the right-hand side is a measure

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Abstract

LetA(u)=−diva(x, u, Du) be a Leray-Lions operator defined onW 1,p0 (Ω) and μ be a bounded Radon measure. For anyu SOLA (Solution Obtained as Limit of Approximations) ofA(u)=μ in Ω,u=0 on ∂Ω, we prove that the truncationsT k(u) at heightk satisfyA(T k(u)) →A(u) in the weak * topology of measures whenk → + ∞.

Résumé

SoitA(u)=−diva(x, u, Du) un opérateur de Leray-Lions défini surW 1,p0 (Ω) et μ une mesure de Radon bornée. Pour toutu SOLA (Solution Obtenue comme Limite d'Approximations) deA(u)=μ dans Ω,u=0 sur ∂Ω, nous démontrons que les troncaturesT k(u) à la hauteurk vérifientA(T k(u)) →A(u) dans la topologie faible * des mesures quandk → + ∞.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma I, Piazzale A. Moro, 00185, Roma, Italia

    Lucio Boccardo

  2. Laboratoire d`Analyse Numérique, Université Paris VI, Tour 55-65, 4 place Jussieu, 75252, Paris Cedex 05, France

    François Murat

Authors
  1. Lucio Boccardo
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  2. François Murat
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Boccardo, L., Murat, F. A property of nonlinear elliptic equations when the right-hand side is a measure. Potential Anal 3, 257–263 (1994). https://doi.org/10.1007/BF01468245

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  • DOI: https://doi.org/10.1007/BF01468245

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