A new graph-directed construction of nonlocal energies on the unit interval
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912274243911680 |
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| 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 |