A family of fundamental solutions for elliptic quaternion coefficient differential operators and application to perturbation results for single layer potentials

In this note we announce some of the results that will be presented in a forthcoming paper by the authors, and which are concerned about the construction of a family of fundamental solutions for elliptic partial differential operators with quaternion constant coefficients. The elements of such a family are functions which depend jointly real analytically on the coefficients of the operators and on the spatial variable. A detailed description of such fundamental solutions has been deduced in order to study regularity and stability properties in the frame of Schauder spaces for the corresponding layer potentials.