Submitted Paper

Inserted: 23 jul 2026
Last Updated: 23 jul 2026

Year: 2026
Doi: 10.13140/RG.2.2.15990.36166

Abstract:

We complete the nonlocal counterpart of Serrin's classical removability criterion ({Acta Math.}, 1964): a relatively closed set is removable if and only if its natural fractional capacity vanishes. The implication from vanishing capacity to removability was proved by Kim and Lee ({arXiv}, 2024), whereas we prove the converse. Thus the capacitary condition is sharp.

Keywords: nonlocal equations, integro-differential operators, removable singularity, isolated singularity