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This article is cited in 11 scientific papers (total in 11 papers)
A quaternionic treatment of the inhomogeneous $\operatorname{div}$-$\operatorname{rot}$ system
F. Colomboa, M. E. Luna-Elizarrarásb, I. Sabadinia, M. Shapirob, D. C. Struppac a Dipartimento di Matematica, Politecnico di Milano, Milano
b Departamento de Matemáticas E.S.F.M. del I.P.N., México, México
c Schmid College of Science, Chapman University, Orange, California
Abstract:
In this paper we study the inhomogeneous div-rot system ($\operatorname{div}\vec f=g_0$, $\operatorname{rot}\vec f=\vec g$) where the datum $(g_0,\vec g)$ 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 $\operatorname{div}$ and $\operatorname{rot}$. 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.
Key words and phrases:
$\operatorname{div}$-$\operatorname{rot}$ system, right inverse operator, algebraic analysis, cohomology vanishing.
Received: August 11, 2010
Citation:
F. Colombo, M. E. Luna-Elizarrarás, I. Sabadini, M. Shapiro, D. C. Struppa, “A quaternionic treatment of the inhomogeneous $\operatorname{div}$-$\operatorname{rot}$ system”, Mosc. Math. J., 12:1 (2012), 37–48
Linking options:
https://www.mathnet.ru/eng/mmj446 https://www.mathnet.ru/eng/mmj/v12/i1/p37
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