Items for "singularly perturbed domain"

Asymptotic behavior of the solutions of the Dirichlet problem for the Laplace operator in a domain with a small hole. A functional analytic approach

We consider a hypersurface in Rⁿ parametrized by a diffeomorphism Φ^o of the unit sphere in Rⁿ into Rⁿ, and we take a point w in the domain I[φ^o] enclosed by the image of Φ^o, and we consider the ‘hole’ I[w+εξ] enclosed by the image of the hypersurface w+εξ, where ξ is a diffeomorphism as Φ^o with 0∈I[ξ] and ε is a small positive real parameter...

Keywords: Dirichlet boundary value problem, singularly perturbed domain, Laplace operator, real analytic continuation in Banach space