Nonlocal-to-local convergence of the $p$-Biharmonic evolution equation with the Dirichlet boundary condition
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910095440347136 |
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| author | Shi, Kehan Ran, Yi |
| author_facet | Shi, Kehan Ran, Yi |
| contents | This paper studies the nonlocal $p$-biharmonic evolution equation with the Dirichlet boundary condition that arises in image processing and data analysis. We prove the existence and uniqueness of solutions to the nonlocal equation and discuss the large time behavior of the solution. By appropriately rescaling the nonlocal kernel, we further show that the solution converges to the solution of the classical $p$-biharmonic equation with the Dirichlet boundary condition. Numerical experiments are presented to demonstrate the effectiveness of the nonlocal $p$-biharmonic equation for image inpainting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal-to-local convergence of the $p$-Biharmonic evolution equation with the Dirichlet boundary condition Shi, Kehan Ran, Yi Analysis of PDEs This paper studies the nonlocal $p$-biharmonic evolution equation with the Dirichlet boundary condition that arises in image processing and data analysis. We prove the existence and uniqueness of solutions to the nonlocal equation and discuss the large time behavior of the solution. By appropriately rescaling the nonlocal kernel, we further show that the solution converges to the solution of the classical $p$-biharmonic equation with the Dirichlet boundary condition. Numerical experiments are presented to demonstrate the effectiveness of the nonlocal $p$-biharmonic equation for image inpainting. |
| title | Nonlocal-to-local convergence of the $p$-Biharmonic evolution equation with the Dirichlet boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.01364 |