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

Leoni, Giovanni, and Morini, Massimiliano. "Necessary and sufficient conditions for the chain rule in $W_{\text{loc}}^{1,1}(\mathbb {R}^N;\mathbb {R}^d)$ and $BV_{\text{loc}}(\mathbb {R}^N;\mathbb {R}^d)$." Journal of the European Mathematical Society 009.2 (2007): 219-252. <http://eudml.org/doc/277442>.

@article{Leoni2007,
abstract = {We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space $W^\{1,1\}_\{\text\{loc\}\}(\mathbb \{R\}^N;\mathbb \{R\}^d)$ and in the space $BV_\{\text\{loc\}\}(\mathbb \{R\}^N;\mathbb \{R\}^d)$ of functions of bounded variation.},
author = {Leoni, Giovanni, Morini, Massimiliano},
journal = {Journal of the European Mathematical Society},
keywords = {chain rule; Sobolev functions; functions of bounded variations; chain rule; Sobolev space; function of bounded variation; differentiability of Lipschitz functions},
language = {eng},
number = {2},
pages = {219-252},
publisher = {European Mathematical Society Publishing House},
title = {Necessary and sufficient conditions for the chain rule in $W_\{\text\{loc\}\}^\{1,1\}(\mathbb \{R\}^N;\mathbb \{R\}^d)$ and $BV_\{\text\{loc\}\}(\mathbb \{R\}^N;\mathbb \{R\}^d)$},
url = {http://eudml.org/doc/277442},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Leoni, Giovanni
AU - Morini, Massimiliano
TI - Necessary and sufficient conditions for the chain rule in $W_{\text{loc}}^{1,1}(\mathbb {R}^N;\mathbb {R}^d)$ and $BV_{\text{loc}}(\mathbb {R}^N;\mathbb {R}^d)$
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 2
SP - 219
EP - 252
AB - We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space $W^{1,1}_{\text{loc}}(\mathbb {R}^N;\mathbb {R}^d)$ and in the space $BV_{\text{loc}}(\mathbb {R}^N;\mathbb {R}^d)$ of functions of bounded variation.
LA - eng
KW - chain rule; Sobolev functions; functions of bounded variations; chain rule; Sobolev space; function of bounded variation; differentiability of Lipschitz functions
UR - http://eudml.org/doc/277442
ER -