Abstract
The aim of this paper is to state a nonautonomous chain rule in BV with Lipschitz dependence, i.e., a formula for the distributional derivative of the composite function \({v(x) = B(x, u(x))}\), where \({u : \mathbb{R}^N \rightarrow \mathbb{R}}\) is a scalar function of bounded variation, \({B(\cdot, t)}\) has bounded variation and \({B(x, \cdot)}\) is only a Lipschitz continuous function. We present a survey of recent developments on the nonautonomous chain rules in BV. Formulas of this type are an useful tool especially in view to applications to lower semicontinuity for integral functional (see [12, 14, 15, 16]) and to the conservation laws with discontinuous flux (see [8, 10, 11]).
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De Cicco, V. Nonautonomous Chain Rules in BV with Lipschitz Dependence. Milan J. Math. 84, 243–267 (2016). https://doi.org/10.1007/s00032-016-0257-2
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DOI: https://doi.org/10.1007/s00032-016-0257-2