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<p>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.</p>

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A Note on Non-local Sobolev Spaces and Non-local Perimeters

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月20日

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  • Konstantinos Bessas,
  • Giuseppe Cosma Brusca

摘要

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.