Volume 56, Number 6, November-December 2022
|Page(s)||1889 - 1910|
|Published online||12 August 2022|
Shape analyticity and singular perturbations for layer potential operators
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: email@example.com
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
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