Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Singular Perturbation
Asymptotics and Difference Schemes
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 March 2026
- Language
- EN
- Document type
- Preprint