A chain rule in L1 (div;Q) and its applications to lower semicontinuity
De Cicco V., De Leoni G.
A chain rule in the space L1 (div;Ω) is obtained under weak regularity conditions.This chain rule has important applications in the study of lower semicontinuityproblems for general functionals of the form ☺Ω f(x, u,∇u) dx with respect to strong convergence in L1 (Ω) . Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.
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