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.
Shape analyticity and singular perturbations for layer potential operators
Luzzini, P;Musolino, P
2022
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.File in questo prodotto:
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