Sobolev spaces on warped products
Functional Analysis
2021-08-17 v2
Abstract
We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: - the characterization of the Sobolev spaces in such products - the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications. The results of this paper have been needed in the recent proof of the `volume-cone-to-metric-cone' property of spaces obtained by the first author and De Philippis.
Keywords
Cite
@article{arxiv.1512.03177,
title = {Sobolev spaces on warped products},
author = {Nicola Gigli and Bang-Xian Han},
journal= {arXiv preprint arXiv:1512.03177},
year = {2021}
}
Comments
Corrected few typos in the previous version and updated the presentation