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A general chain rule for distributional derivatives


Authors: L. Ambrosio and G. Dal Maso
Journal: Proc. Amer. Math. Soc. 108 (1990), 691-702
MSC: Primary 26B30; Secondary 46F10, 49F22
DOI: https://doi.org/10.1090/S0002-9939-1990-0969514-3
MathSciNet review: 969514
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Abstract: We prove a general chain rule for the distribution derivatives of the composite function $ \upsilon (x) = f(u(x))$, where $ u:{{\mathbf{R}}^n} \to {{\mathbf{R}}^m}$ has bounded variation and $ f:{{\mathbf{R}}^m} \to {{\mathbf{R}}^k}$ is Lipschitz continuous.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0969514-3
Article copyright: © Copyright 1990 American Mathematical Society

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