Necessary and sufficient conditions for the chain rule in $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^N; \mathbb{R})$ and $BV_{\mathrm{loc}}(\mathbb{R}^N; \mathbb{R}^d)$

Giovanni Leoni; Massimiliano Morini

doi:10.4171/jems/78

Geodesic

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Necessary and sufficient conditions for the chain rule in $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^N; \mathbb{R})$ and $BV_{\mathrm{loc}}(\mathbb{R}^N; \mathbb{R}^d)$

Giovanni Leoni ; Massimiliano Morini

Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 219-252.

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Résumé

In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

DOI : 10.4171/jems/78

Classification : 46-XX, 26-XX, 28-XX, 00-XX
Keywords: Chain rule, Sobolev functions, functions of bounded variations

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     title = {Necessary and sufficient conditions for the chain rule in $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^N; \mathbb{R})$ and $BV_{\mathrm{loc}}(\mathbb{R}^N; \mathbb{R}^d)$},
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Giovanni Leoni; Massimiliano Morini. Necessary and sufficient conditions for the chain rule in $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^N; \mathbb{R})$ and $BV_{\mathrm{loc}}(\mathbb{R}^N; \mathbb{R}^d)$. Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 219-252. doi : 10.4171/jems/78. http://geodesic.mathdoc.fr/articles/10.4171/jems/78/

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