A local and nonlocal coupling model involving the $p$-Laplacian
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909988224499712 |
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| author | Kaufmann, Uriel Vidal, Raúl |
| author_facet | Kaufmann, Uriel Vidal, Raúl |
| contents | In this paper we extend some results presented in \cite{julio} to the case of the $p$-Laplacian operator. More precisely, we consider a model that couples a local $p$-Laplacian operator with a nonlocal $p$-Laplacian operator through source terms in the equation. The resulting problem is associated with an energy functional. We establish the existence and uniqueness of a solution, which is obtained via the direct minimization of the corresponding energy functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A local and nonlocal coupling model involving the $p$-Laplacian Kaufmann, Uriel Vidal, Raúl Analysis of PDEs 35R11, 45K05, 47G20 In this paper we extend some results presented in \cite{julio} to the case of the $p$-Laplacian operator. More precisely, we consider a model that couples a local $p$-Laplacian operator with a nonlocal $p$-Laplacian operator through source terms in the equation. The resulting problem is associated with an energy functional. We establish the existence and uniqueness of a solution, which is obtained via the direct minimization of the corresponding energy functional. |
| title | A local and nonlocal coupling model involving the $p$-Laplacian |
| topic | Analysis of PDEs 35R11, 45K05, 47G20 |
| url | https://arxiv.org/abs/2508.20951 |