Proceedings (submitted)
Inserted: 8 apr 2025
Last Updated: 8 apr 2025
Year: 2025
Abstract:
We investigate the space of non-local Sobolev functions associated with an integral kernel. We prove an extension result, Sobolev and Poincaré 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.
Keywords: isoperimetric problems, Non-local Sobolev spaces, Functions of non-local bounded variation, Non-local interactions, Non-local perimeters
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