Finsler $p$-Laplacian in domains becoming unbounded
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918037253259264 |
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| author | Esposito, Luca Lamberti, Lorenzo N., Dattatreya N. Roy, Prosenjit |
| author_facet | Esposito, Luca Lamberti, Lorenzo N., Dattatreya N. Roy, Prosenjit |
| contents | We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler $p$-Laplace operator, also known as the anisotropic $p$-Laplace operator on a sequence of bounded cylinders whose length tends to infinity. We prove that the solutions on the bounded cylinders converge to the solution on the cross-section, with a polynomial rate of convergence in the general case and exponential convergence in some special cases. We show that energies on finite cylinders, with the multiplication of a scaling factor, converge to the energy on the cross-section. Finally, we investigate the convergence of the first eigenvalue and, for a specific subclass, we provide the optimal convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finsler $p$-Laplacian in domains becoming unbounded Esposito, Luca Lamberti, Lorenzo N., Dattatreya N. Roy, Prosenjit Analysis of PDEs We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler $p$-Laplace operator, also known as the anisotropic $p$-Laplace operator on a sequence of bounded cylinders whose length tends to infinity. We prove that the solutions on the bounded cylinders converge to the solution on the cross-section, with a polynomial rate of convergence in the general case and exponential convergence in some special cases. We show that energies on finite cylinders, with the multiplication of a scaling factor, converge to the energy on the cross-section. Finally, we investigate the convergence of the first eigenvalue and, for a specific subclass, we provide the optimal convergence rate. |
| title | Finsler $p$-Laplacian in domains becoming unbounded |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.22329 |