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