A perturbation result for the layer potentials ofgeneral second order differential operators with constant coefficients

We consider a hypersurface in Euclidean space ${\mathbb{R}}^{n}$ parame\-trized by a diffeomorphism of the boundary of a regular domain in ${\mathbb{R}}^{n}$ to ${\mathbb{R}}^{n}$, and a density function on the hypersurface, which we think as points in suitable Schauder spaces, and a family of second order differential operators with constant coefficients and a corresponding family of fundamental solutions depending on a parameter. Then we investigate the dependence of the corresponding layer potentials, which we also think as points in suitable Schauder spaces, upon variation of the diffeomorphism and of the density and of the parameter, and we show a real analyticity theorem for such a dependence.