Abstract
The heat transfer problem in isotropic media has been studied extensively in Clifford analysis, but very little in the anisotropic case for this setting. As a first step in this way, we introduce in this work Dirac operators with weights belonging to the Clifford algebra \({\mathcal {A}}_n\), which factor the second order elliptic differential operator \( {\tilde{\Delta }}_n= div (B \,\nabla ), \) where \(B \in \mathbb {R}^{n \times n}\) is a symmetric and positive definite matrix. For these weighted Dirac operators we construct fundamental solutions and get a Borel–Pompeiu and Cauchy integral formula.
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Communicated by Helmuth Robert Malonek.
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Vanegas, J., Vargas, F. On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media. Adv. Appl. Clifford Algebras 28, 46 (2018). https://doi.org/10.1007/s00006-018-0860-0
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DOI: https://doi.org/10.1007/s00006-018-0860-0