LAUSR

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 $${\mathcal {A}}_n$$An, which factor the second order elliptic differential operator $$ {\tilde{\Delta }}_n= div (B \,\nabla ), $$Δ~n=div(B∇), where $$B \in \mathbb {R}^{n \times n}$$B∈Rn×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.