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arXiv · 2603.03032

Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary

Naísa C. Garcia·Raquel Lehrer·Marcus A. M. Marrocos
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Abstract

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.

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Naísa C. Garcia, Raquel Lehrer, Marcus A. M. Marrocos. 2026-03-03. Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary. https://arxiv.org/abs/2603.03032

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