The div-curl lemma trente ans après : an extension and an application to the G-convergence of unbounded monotone operators
By Marc Briane, J. Casado-díaz, François Murat. 2009
48 citations recorded by the source corpus.
In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn where the sequences vn and wn are respectively bounded in Lp(Ω)N and Lq(Ω)N, while divvn and curlwn are compact in some Sobolev spaces, under the condition 1⩽1p+1q⩽1+1N. Our approach is based on a suitable decomposition of the functions vn and wn, 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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/7886761636e9e5bc1a5f9619c90b1d446137ff3f
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In Applied Mathematics
Citations in the corpus
- The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1} (2009, background): “The div–curl lemma is the cornerstone of the theory of compensated compactness which was developed by Murat and Tartar in the late seventies [13, 14, 16, 17, 18], and is still a very active area of research [ 5 ].”