A note on non-local Sobolev spaces and non-local perimeters
Functional Analysis
2025-04-09 v1 Analysis of PDEs
Abstract
We investigate the space of non-local Sobolev functions associated with an integral kernel. We prove an extension result, Sobolev and Poincar\'e inequalities and an isoperimetric inequality for the non-local perimeter restricted to a set. Finally, we remark on non-local isoperimetric problems, even when the underlying kernel is not necessarily radially symmetric.
Cite
@article{arxiv.2504.06236,
title = {A note on non-local Sobolev spaces and non-local perimeters},
author = {Konstantinos Bessas and Giuseppe Cosma Brusca},
journal= {arXiv preprint arXiv:2504.06236},
year = {2025}
}
Comments
24 pages. Conference proceedings