A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients

M. Dalla Riva*, J. Morais, P. Musolino

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)

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.

Original languageEnglish
Pages (from-to)1569-1582
Number of pages14
JournalMathematical Methods in the Applied Sciences
Volume36
Issue number12
Early online date06 Dec 2012
DOIs
Publication statusPublished - 01 Aug 2013

Keywords

  • elliptic partial differential operators with quaternion constant coefficients
  • fundamental solutions
  • layer potentials
  • quaternion analysis

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