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We study the effect of regular and singular domain perturbations on layerpotential operators for the Laplace equation. First, we consider layerpotentials supported on a diffeomorphic image $\phi(\partial\Omega)$ of areference set $\partial\Omega$ and we present some real analyticity results forthe dependence upon the map $\phi$. Then we introduce a perforated domain$\Omega(\epsilon)$ with a small hole of size $\epsilon$ and we compute powerseries expansions that describe the layer potentials on$\partial\Omega(\epsilon)$ when the parameter $\epsilon$ approximates thedegenerate value $\epsilon=0$.

Shape analyticity and singular perturbations for layer potential operators