A Nonlocal $p$-Laplacian Interface Model with Sharp Interface
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910275805904896 |
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| author | Shi, Kehan Shi, Zuoqiang Wang, Tangjun |
| author_facet | Shi, Kehan Shi, Zuoqiang Wang, Tangjun |
| contents | We propose an energy-based nonlocal $p$-Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced through a penalty term. A key feature is that the model retains a sharp interface, which facilitates extension to other interface problems; we illustrate this by developing a nonlocal approximation for the $p$-Laplacian interface problem with membrane conditions. By establishing $Γ$-convergence and compactness, we prove that as the nonlocal horizon vanishes, minimizers of the nonlocal functionals converge to those of the local counterparts. Numerical experiments using an efficient finite element method confirm the convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Nonlocal $p$-Laplacian Interface Model with Sharp Interface Shi, Kehan Shi, Zuoqiang Wang, Tangjun Analysis of PDEs Numerical Analysis We propose an energy-based nonlocal $p$-Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced through a penalty term. A key feature is that the model retains a sharp interface, which facilitates extension to other interface problems; we illustrate this by developing a nonlocal approximation for the $p$-Laplacian interface problem with membrane conditions. By establishing $Γ$-convergence and compactness, we prove that as the nonlocal horizon vanishes, minimizers of the nonlocal functionals converge to those of the local counterparts. Numerical experiments using an efficient finite element method confirm the convergence. |
| title | A Nonlocal $p$-Laplacian Interface Model with Sharp Interface |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2606.00594 |