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 originale | Inglese |
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pagine (da-a) | 1889-1910 |
Numero di pagine | 22 |
Rivista | ESAIM: Mathematical Modelling and Numerical Analysis |
Volume | 56 |
Numero di pubblicazione | 6 |
DOI | |
Stato di pubblicazione | Pubblicato - 2022 |
Keywords
- Laplace operator
- Single layer potential
- asymptotic behavior
- domain perturbation
- double layer potential
- perforated domain
- shape sensitivity analysis
- special nonlinear operators