A note on non-local Sobolev spaces and non-local perimeters (2504.06236v1)

Published 8 Apr 2025 in math.FA and math.AP

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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