  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 $\epsilon=0$.
