Biting theorems for Jacobians and their applications

Abstract Weak continuity for sequences of Jacobians of vector-valued functions in W1,n(Ω; Rn) in the sense of Chacon’s Biting Lemma [13] is established via a maximal function method developed by Acerbi and Fusco [1]. A « div-curl » Lemma in the same spirit is also proved. The results are applied to the existence problem of nonlinear elastostatics and to a problem involving rank-one connections appearing in the theory of phase transitions.

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