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 imageϕ(∂Ω) of a reference set ∂Ω and we present some real analyticity results for the dependence upon the mapϕ. Then we introduce a perforated domain Ω(ε) with a small hole of sizeεand we compute power series expansions that describe the layer potentials on ∂Ω(ε) when the parameterεapproximates the degenerate valueε = 0.
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