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The div-curl lemma "trente ans apres": an extension and an application to the G-convergence of unbounded monotone operators

Abstract : In this paper new div-curl results are derived. For any open set Omega of R-N, N >= 2, we study the limit of the product v(n) . w(n) where the sequences v(n) and w(n) are respectively bounded in L-p(Omega)(N) and L-q(Omega)(N), while div v(n) and curl w(n) are compact in some Sobolev spaces, under the condition 1 <= 1/p + 1/q <= 1 + 1/N. Our approach is based on a suitable decomposition of the functions v(n) and w(n), combined with the concentration compactness of P.-L. Lions and a recent result of H. Brezis and J. Van Schaftingen. As a consequence we obtain a new result of G-convergence for unbounded monotone operators of N-Laplacian type.
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https://hal.archives-ouvertes.fr/hal-00434936
Contributor : Maryse Collin <>
Submitted on : Monday, November 23, 2009 - 2:27:26 PM
Last modification on : Monday, July 6, 2020 - 3:38:05 PM

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Marc Briane, Juan Casado-Diaz, François Murat. The div-curl lemma "trente ans apres": an extension and an application to the G-convergence of unbounded monotone operators. Journal de Mathématiques Pures et Appliquées, Elsevier, 2009, 91 (5), pp.476-494. ⟨10.1016/j.matpur.2009.01.002⟩. ⟨hal-00434936⟩

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