Shape analyticity and singular perturbations for layer potential operators

Matteo Dalla Riva; Paolo Luzzini; Paolo Musolino

doi:10.1051/m2an/2022057

Shape analyticity and singular perturbations for layer potential operators

Matteo Dalla Riva
, Paolo Luzzini
, Paolo Musolino

Research output: Contribution to journal › Article › peer-review

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 (Ω) of a reference set Ω and we present some real analyticity results for the dependence upon the map. 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.

Original language	English
Pages (from-to)	1889-1910
Number of pages	22
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	56
Issue number	6
DOIs	https://doi.org/10.1051/m2an/2022057
Publication status	Published - 1 Nov 2022
Externally published	Yes

Keywords

Asymptotic behavior
Domain perturbation
Double layer potential
Laplace operator
Perforated domain
Shape sensitivity analysis
Single layer potential
Special nonlinear operators

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10.1051/m2an/2022057

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title = "Shape analyticity and singular perturbations for layer potential operators",

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 (Ω) of a reference set Ω and we present some real analyticity results for the dependence upon the map. 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 = "Asymptotic behavior, Domain perturbation, Double layer potential, Laplace operator, Perforated domain, Shape sensitivity analysis, Single layer potential, Special nonlinear operators",

author = "\{Dalla Riva\}, Matteo and Paolo Luzzini and Paolo Musolino",

note = "Publisher Copyright: {\textcopyright} The authors. Published by EDP Sciences, SMAI 2022.",

year = "2022",

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doi = "10.1051/m2an/2022057",

language = "English",

volume = "56",

pages = "1889--1910",

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TY - JOUR

T1 - Shape analyticity and singular perturbations for layer potential operators

AU - Dalla Riva, Matteo

AU - Luzzini, Paolo

AU - Musolino, Paolo

N1 - Publisher Copyright: © The authors. Published by EDP Sciences, SMAI 2022.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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 (Ω) of a reference set Ω and we present some real analyticity results for the dependence upon the map. 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.

AB - 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 (Ω) of a reference set Ω and we present some real analyticity results for the dependence upon the map. 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.

KW - Asymptotic behavior

KW - Domain perturbation

KW - Double layer potential

KW - Laplace operator

KW - Perforated domain

KW - Shape sensitivity analysis

KW - Single layer potential

KW - Special nonlinear operators

UR - https://www.scopus.com/pages/publications/85137094582

U2 - 10.1051/m2an/2022057

DO - 10.1051/m2an/2022057

M3 - Article

SN - 2822-7840

VL - 56

SP - 1889

EP - 1910

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

IS - 6

ER -

Shape analyticity and singular perturbations for layer potential operators

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Keywords

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