Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912402548719616 |
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| author | Dattatreya, N. N. |
| author_facet | Dattatreya, N. N. |
| contents | In this article, we study the asymptotic behavior of large solutions for a quasi-linear equation involving the p-Laplacian, defined on a sequence of finite cylindrical domains converging to an infinite cylinder. We demonstrate that the sequence of solutions converges locally, in the Sobolev norm, to a solution of the corresponding cross-sectional problem. Moreover, we establish a convergence rate. As part of our analysis, we extend existing convergence results for the case $p\geq 2$, which previously lacked explicit convergence rates, to the range $1<p<2$. We additionally address solutions with finite Dirichlet boundary data within a unified framework and exhibit that this rate of convergence is independent of the boundary data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded Dattatreya, N. N. Analysis of PDEs 35J62, 35J92, 35J25, 35A01 In this article, we study the asymptotic behavior of large solutions for a quasi-linear equation involving the p-Laplacian, defined on a sequence of finite cylindrical domains converging to an infinite cylinder. We demonstrate that the sequence of solutions converges locally, in the Sobolev norm, to a solution of the corresponding cross-sectional problem. Moreover, we establish a convergence rate. As part of our analysis, we extend existing convergence results for the case $p\geq 2$, which previously lacked explicit convergence rates, to the range $1<p<2$. We additionally address solutions with finite Dirichlet boundary data within a unified framework and exhibit that this rate of convergence is independent of the boundary data. |
| title | Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded |
| topic | Analysis of PDEs 35J62, 35J92, 35J25, 35A01 |
| url | https://arxiv.org/abs/2505.23600 |