A Quaternionic Treatment of the Inhomogeneous Div-rot System

Authors

Fabrizio Colombo, Politecnico di Milano
M. E. Luna-Elizarrarás, IPNFollow
Irene Sabadini, Politecnico di Milano
M. Shapiro, IPNFollow
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

2012

Abstract

In this paper we study the inhomogeneous div-rot system (div ~f = g0, rot ~f = ~g) where the datum (g0, ~g) consists of a continuous scalar and a continuous vector field, respectively. We embed the system in its appropriate quaternionic setting, and by using the right inverse of the Moisil–Teodorescu operator, we provide a necessary and sufficient condition for the solvability of the system and we describe its general solution. As a byproduct we obtain an explicit integral expression for the right inverse for the operators div and rot. Finally, we show how the same problem could have been studied using algebraic analysis, and we use this different approach to obtain some additional results.

Comments

This article was originally published in Moscow Mathematical Journal , volume 12, issue 1, in 20-12.

Recommended Citation

Colombo, F., Luna-Elizarraras, M.E., Sabadini, I., Shapiro, M., & Struppa, D.C. (2012). A quaternionic treatment of the inhomogenous div-rot system. Moscow Mathematical Journal, 12(1), 37-48.

Peer Reviewed

1

Copyright

Independent University (Moscow)