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arXiv · 2504.06236

A note on non-local Sobolev spaces and non-local perimeters

Konstantinos Bessas·Giuseppe Cosma Brusca
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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.

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Konstantinos Bessas, Giuseppe Cosma Brusca. 2025-04-08. A note on non-local Sobolev spaces and non-local perimeters. https://arxiv.org/abs/2504.06236

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