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(∂Ω) of a reference set ∂Ω 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 ∂Ω(ε) when the parameter ε approximates the degenerate value ε = 0.
Keywords: Single layer potential, double layer potential, Laplace operator, domain perturbation, shape sensitivity analysis, perforated domain, asymptotic behavior, special nonlinear operators
@article{M2AN_2022__56_6_1889_0,
author = {Dalla Riva, Matteo and Luzzini, Paolo and Musolino, Paolo},
title = {Shape analyticity and singular perturbations for layer potential operators},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1889--1910},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {6},
doi = {10.1051/m2an/2022057},
mrnumber = {4467103},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022057/}
}
TY - JOUR AU - Dalla Riva, Matteo AU - Luzzini, Paolo AU - Musolino, Paolo TI - Shape analyticity and singular perturbations for layer potential operators JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1889 EP - 1910 VL - 56 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022057/ DO - 10.1051/m2an/2022057 LA - en ID - M2AN_2022__56_6_1889_0 ER -
%0 Journal Article %A Dalla Riva, Matteo %A Luzzini, Paolo %A Musolino, Paolo %T Shape analyticity and singular perturbations for layer potential operators %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1889-1910 %V 56 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022057/ %R 10.1051/m2an/2022057 %G en %F M2AN_2022__56_6_1889_0
Dalla Riva, Matteo; Luzzini, Paolo; Musolino, Paolo. Shape analyticity and singular perturbations for layer potential operators. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 6, pp. 1889-1910. doi: 10.1051/m2an/2022057
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