A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

Abstract:

In the present paper we use the piecewise constant structure relations of a Clifford algebra in order to obtain a Cauchy-Pompeiu representation for D - λ and D + λ operators, with these formulas we construct a distributional solutions for the equations that involves these operators with arbitrary right hand side. We also present an example where we build an integral representation for combinations of these operators. © 2012 Springer Basel.

Año de publicación:

2013

Keywords:

• Integral representation
• Cauchy-Pompeiu Formula
• Clifford analysis
• Structure relations of Clifford algebra
• fundamental solution

Fuente:

scopus