Year: 2022
Type: preprint
Abstract: We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $ϕ(\partialΩ)$ of a reference set $\partialΩ$ and we present some real analyticity results for the dependence upon the map $ϕ$. Then we introduce a perforated domain $Ω(ε)$ with a small hole of size $ε$ and we compute power series expansions that describe the layer potentials on $\partialΩ(ε)$ when the parameter $ε$ approximates the degenerate value $ε=0$.
Source: arXiv (Cornell University)
Institutions: University of Padua, Ca' Foscari University of Venice
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226512041