| Issue |
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
|
|
|---|---|---|
| Page(s) | 1889 - 1910 | |
| DOI | https://doi.org/10.1051/m2an/2022057 | |
| Published online | 12 August 2022 | |
Shape analyticity and singular perturbations for layer potential operators
1
Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale delle Scienze, Ed. 8, 90128 Palermo, Italy
2
Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy
3
Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Via Torino 155, 30172 Venezia Mestre, Italy
* Corresponding author: pluzzini@math.unipd.it
Received:
3
March
2022
Accepted:
24
June
2022
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.
Mathematics Subject Classification: 31B10 / 35J05 / 47H30 / 35J25 / 45A05
Key words: Single layer potential / double layer potential / Laplace operator / domain perturbation / shape sensitivity analysis / perforated domain / asymptotic behavior / special nonlinear operators
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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