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.
A Note on Non-local Sobolev Spaces and Non-local Perimeters / Bessas, K., Brusca, G.C.. - In: LA MATEMATICA. - ISSN 2730-9657. - 4:4(2025), pp. 829-860. [10.1007/s44007-025-00175-9]
A Note on Non-local Sobolev Spaces and Non-local Perimeters
Brusca, Giuseppe Cosma
2025-01-01
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.File in questo prodotto:
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