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Singularity removal in nonlocal operator inequalities on domains and applications
Abstract
We prove that certain classes of nonlocal integral estimates on domains, involving operators, may be reduced to the local analogues without the singular weight on cubes. The theory applies to two-sided inverse doubling and quasi-monotone kernels with some moment conditions, and with a left-hand-side operator with average domain-bi-Lipschitz properties. Direct applications to fractional semi-norm inequalities in Peridynamics, such as fractional Korn's inequalities and Geometric Rigidity Estimates are presented.
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BibTeX
@misc{harutyunyan2026singularity,
title = {{Singularity removal in nonlocal operator inequalities on domains and applications}},
author = {Davit Harutyunyan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39437},
eprint = {2610.39437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39437},
}
RIS
TY - UNPB
TI - Singularity removal in nonlocal operator inequalities on domains and applications
AU - Davit Harutyunyan
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39437
UR - https://arxiv.org/abs/2610.39437
AB - We prove that certain classes of nonlocal integral estimates on domains, involving operators, may be reduced to the local analogues without the singular weight on cubes. The theory applies to two-sided inverse doubling and quasi-monotone kernels with some moment conditions, and with a left-hand-side operator with average domain-bi-Lipschitz properties. Direct applications to fractional semi-norm inequalities in Peridynamics, such as fractional Korn's inequalities and Geometric Rigidity Estimates are presented.
ER -