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

Giovanni Leoni; Massimiliano Morini

Journal of the European Mathematical Society (2007)

- Volume: 009, Issue: 2, page 219-252
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topLeoni, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.