Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary
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| Format: | Preprint |
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2026
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| _version_ | 1866911482476756992 |
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| author | Garcia, Naísa C. Lehrer, Raquel Marrocos, Marcus A. M. |
| author_facet | Garcia, Naísa C. Lehrer, Raquel Marrocos, Marcus A. M. |
| contents | In this work we analyse the convergence of solutions of the Poisson equation with Neumann boundary conditions in a thin domain with highly oscillatory behavior $\mathcal{U}^\varepsilon$ contained in the sphere $\mathbb{S}^2$. Using the Multiple Scales method, we obtain the homogenized limit problem and analyse the convergence of solutions, as $\varepsilon$ tends to $0$. Introducing appropriate correctors, we show strong convergence and give error estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_03032 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary Garcia, Naísa C. Lehrer, Raquel Marrocos, Marcus A. M. Analysis of PDEs 5B25, 35B27, 74Q05 In this work we analyse the convergence of solutions of the Poisson equation with Neumann boundary conditions in a thin domain with highly oscillatory behavior $\mathcal{U}^\varepsilon$ contained in the sphere $\mathbb{S}^2$. Using the Multiple Scales method, we obtain the homogenized limit problem and analyse the convergence of solutions, as $\varepsilon$ tends to $0$. Introducing appropriate correctors, we show strong convergence and give error estimates. |
| title | Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary |
| topic | Analysis of PDEs 5B25, 35B27, 74Q05 |
| url | https://arxiv.org/abs/2603.03032 |