Shape analyticity and singular perturbations for layer potential operators

Matteo Dalla Riva; Paolo Luzzini; Paolo Musolino

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arXiv · 2203.01836

Shape analyticity and singular perturbations for layer potential operators

Matteo Dalla Riva·Paolo Luzzini·Paolo Musolino

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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 $\phi(\partial\Omega)$ of a reference set $\partial\Omega$ 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 $\partial\Omega(\epsilon)$ when the parameter $\epsilon$ approximates the degenerate value $\epsilon=0$.

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Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino. 2022-03-03. Shape analyticity and singular perturbations for layer potential operators. https://arxiv.org/abs/2203.01836

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