JournalsjemsVol. 9, No. 2pp. 219–252

Necessary and sufficient conditions for the chain rule in <em>W<sub>loc</sub><sup>1,1</sup>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>) and BV<sub>loc</sub>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>)</em>

  • Giovanni Leoni

    Carnegie-Mellon University, Pittsburgh, USA
  • Massimiliano Morini

    Carnegie Mellon University, Pittsburgh, United States
Necessary and sufficient conditions for the chain rule in <em>W<sub>loc</sub><sup>1,1</sup>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>) and BV<sub>loc</sub>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>)</em> cover
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Abstract

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.

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Giovanni Leoni, Massimiliano Morini, Necessary and sufficient conditions for the chain rule in <em>W<sub>loc</sub><sup>1,1</sup>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>) and BV<sub>loc</sub>(<strong>R</strong><sup>N</sup>; <strong>R</strong><sup>d</sup>)</em>. J. Eur. Math. Soc. 9 (2007), no. 2, pp. 219–252

DOI 10.4171/JEMS/78