Sobolev space of functions valued in a monotone Banach family
Functional Analysis
2021-02-16 v1 Analysis of PDEs
Abstract
We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a family of Banach spaces. In this case we adapt the definition of Newtonian spaces. For a monotone family, we show the existence of weak derivative, obtain an isomorphism to the standard Sobolev space, and provide some scalar characteristics.
Cite
@article{arxiv.2003.10657,
title = {Sobolev space of functions valued in a monotone Banach family},
author = {Nikita Evseev and Alexander Menovschikov},
journal= {arXiv preprint arXiv:2003.10657},
year = {2021}
}
Comments
23 pages, 3 figures