On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media

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 A<inf>n</inf>, which factor the second order elliptic differential operator Δ~n=div(B∇), where 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.

Año de publicación:

2018

Keywords:

• Clifford algebras depending on parameters
• Fundamental solutions
• Second-order elliptic equations

Fuente:

scopus