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Subjects
26-XX Real functions
26Bxx Functions of several variables
26B40 Representation and superposition of functions

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Necessary and sufficient conditions for the chain rule in $W_{loc}^{1, 1} (ℝ^{N}; ℝ^{d})$ and $B V_{loc} (ℝ^{N}; ℝ^{d})$

Giovanni Leoni, Massimiliano Morini (2007)

Journal of the European Mathematical Society

We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space $W_{loc}^{1, 1} (ℝ^{N}; ℝ^{d})$ and in the space $B V_{loc} (ℝ^{N}; ℝ^{d})$ of functions of bounded variation.

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Displaying 1 – 1 of 1

Necessary and sufficient conditions for the chain rule in W loc 1 , 1 ( ℝ N ; ℝ d ) and B V loc ( ℝ N ; ℝ d )

Currently displaying 1 – 1 of 1

Necessary and sufficient conditions for the chain rule in $W_{loc}^{1, 1} (ℝ^{N}; ℝ^{d})$ and $B V_{loc} (ℝ^{N}; ℝ^{d})$