Vector-valued Sobolev spaces based on Banach function spaces
Functional Analysis
2020-09-22 v1
Abstract
It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree. As well we revise the difference quotient criterion and the property of Lipschitz mapping to preserve Sobolev space when it acting as a superposition operator.
Keywords
Cite
@article{arxiv.2009.09686,
title = {Vector-valued Sobolev spaces based on Banach function spaces},
author = {Nikita Evseev},
journal= {arXiv preprint arXiv:2009.09686},
year = {2020}
}