A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients. (English) Zbl 1277.35011
Summary: The purpose of this paper is to construct a family of fundamental solutions for elliptic partial differential operators with quaternion constant coefficients. The elements of such family are expressed by means of functions, which depend jointly real analytically on the coefficients of the operators and on the spatial variable. We show some regularity properties in the frame of Schauder spaces for the corresponding single layer potentials. Ultimately, we exploit our construction by showing a real analyticity result for perturbations of the layer potentials corresponding to complex elliptic partial differential operators of order two.
MSC:
| 35A08 | Fundamental solutions to PDEs |
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) |
| 35J08 | Green’s functions for elliptic equations |
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