Shape analyticity and singular perturbations for layer potential operators

M Dalla Riva, PAOLO LUZZINI, P Musolino

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer 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 phi( partial differential omega) of a reference set partial differential omega and we present some real analyticity results for the dependence upon the map phi. Then we introduce a perforated domain omega(epsilon) with a small hole of size epsilon and we compute power series expansions that describe the layer potentials on partial differential omega(epsilon) when the parameter epsilon approximates the degenerate value epsilon = 0.
Lingua originaleInglese
pagine (da-a)1889-1910
Numero di pagine22
RivistaESAIM: Mathematical Modelling and Numerical Analysis
Volume56
Numero di pubblicazione6
DOI
Stato di pubblicazionePubblicato - 2022

Keywords

  • Laplace operator
  • Single layer potential
  • asymptotic behavior
  • domain perturbation
  • double layer potential
  • perforated domain
  • shape sensitivity analysis
  • special nonlinear operators

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