A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients |
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Authors: | M Dalla Riva J Morais P Musolino |
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Institution: | 1. Centro de Investiga??o e Desenvolvimento em Matemática e Aplica??es (CIDMA), Universidade de Aveiro, , 3810‐193 Aveiro, Portugal;2. Institut de Recherche Mathématiques de Rennes (IRMAR), Université de Rennes 1, , 263 Avenue du General Leclerc, 35042 Rennes, France |
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Abstract: | 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. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | fundamental solutions quaternion analysis elliptic partial differential operators with quaternion constant coefficients layer potentials |
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