Abstract
In this paper new div-curl results are derived. For any open set Ω 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 ( Ω ) N and L q ( Ω ) 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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