A new graph-directed construction of nonlocal energies on the unit interval

Fuente: arXiv
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Hauptverfasser: Aboud, Anna, Ruiz, Patricia Alonso, Vaughan, Mary
Format: Preprint
Veröffentlicht: 2025
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_version_ 1866912274243911680
author Aboud, Anna
Ruiz, Patricia Alonso
Vaughan, Mary
author_facet Aboud, Anna
Ruiz, Patricia Alonso
Vaughan, Mary
contents We present an analytic construction of nonlocal energies on the unit interval. The energies are defined using a new graph-directed construction of discrete energies on dyadic approximations of the interval. When the discrete jump kernels are comparable to the kernel of the fractional discrete Laplacian, we prove that the discrete energies Mosco converge and the limiting energy is equivalent to the fractional Gagliardo seminorm.
format Preprint
id arxiv_https___arxiv_org_abs_2503_10948
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A new graph-directed construction of nonlocal energies on the unit interval
Aboud, Anna
Ruiz, Patricia Alonso
Vaughan, Mary
Analysis of PDEs
Functional Analysis
35R11, 31C25, 28A80, 49J45
We present an analytic construction of nonlocal energies on the unit interval. The energies are defined using a new graph-directed construction of discrete energies on dyadic approximations of the interval. When the discrete jump kernels are comparable to the kernel of the fractional discrete Laplacian, we prove that the discrete energies Mosco converge and the limiting energy is equivalent to the fractional Gagliardo seminorm.
title A new graph-directed construction of nonlocal energies on the unit interval
topic Analysis of PDEs
Functional Analysis
35R11, 31C25, 28A80, 49J45
url https://arxiv.org/abs/2503.10948