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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.09700 |
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| _version_ | 1866908904373354496 |
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| author | García-Sáez, Guillermo |
| author_facet | García-Sáez, Guillermo |
| contents | From the recent developing of nonlocal gradients with finite horizon $δ>0$ based on general kernels, we introduce a new nonlocal $p$-Laplacian and study the eigenvalue problem associated with it. Furthermore, by virtue of $Γ$-convergence arguments, we establish stability results of the solutions for varying horizon in the extreme cases $δ\to 0^+$ and $δ\to\infty$, recovering the solutions for the local eigenvalue problem associated with the $p$-Laplacian, and the ones associated with the $H^{s,p}$-Laplacian, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of variational eigenvalues for a general nonlocal $p$-Laplacian with varying horizon García-Sáez, Guillermo Analysis of PDEs Spectral Theory From the recent developing of nonlocal gradients with finite horizon $δ>0$ based on general kernels, we introduce a new nonlocal $p$-Laplacian and study the eigenvalue problem associated with it. Furthermore, by virtue of $Γ$-convergence arguments, we establish stability results of the solutions for varying horizon in the extreme cases $δ\to 0^+$ and $δ\to\infty$, recovering the solutions for the local eigenvalue problem associated with the $p$-Laplacian, and the ones associated with the $H^{s,p}$-Laplacian, respectively. |
| title | Asymptotics of variational eigenvalues for a general nonlocal $p$-Laplacian with varying horizon |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2601.09700 |