abstract 80

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

80

Cauchy-Pompeiu type integral formula for multi-harmonic functions

Johan Ceballos, Mariana Ceballos, Antonio Di Teodoro, Daniel González, Diego Ochoa-Tocachi

In the present work, we use a multi-dimensional Clifford type algebra to construct a Cauchy-Pompeiu type integral formula for multi-harmonic functions (also called separately-harmonic functions), which are defined in the domain of $\mathbb{R}^{m_{1}+1}\times\mathbb{R}^{m_{2}+1}\times\cdots\times\mathbb{R}^{m_{n}+1}$. For this purpose, we use the fundamental solution for some second order elliptic operators constructed using the non-Euclidean distance. Finally, we show how we can obtain a Cauchy type formula using iterations.

Keywords: Clifford-type algebra; harmonic functions; multi-dimensional Clifford algebra; multi-harmonic functions; Cauchy-Pompeiu type integral; fundamental solution.

Cite this paper:

Ceballos J., Ceballos M., Di Teodoro A., González D., Ochoa-Tocachi D. 

Cauchy-Pompeiu type integral formula for multi-harmonic functions.

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 11, No.1 pp.75-102, 2023.