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Mosc. Math. J., 2012, Volume 12, Number 1, Pages 37–48 (Mi mmj446)  

This article is cited in 4 scientific papers (total in 4 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.

DOI: https://doi.org/10.17323/1609-4514-2012-12-1-37-48

Full text: http://www.ams.org/.../abst12-1-2012.html
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Bibliographic databases:

MSC: 47F05, 47G10, 35F05
Received: August 11, 2010
Language:

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

Citation in format AMSBIB
\Bibitem{ColLunSab12}
\by F.~Colombo, M.~E.~Luna-Elizarrar\'as, I.~Sabadini, M.~Shapiro, D.~C.~Struppa
\paper A quaternionic treatment of the inhomogeneous $\operatorname{div}$-$\operatorname{rot}$ system
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 37--48
\mathnet{http://mi.mathnet.ru/mmj446}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-37-48}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952424}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309364900003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Luna-Elizarraras M.E., Shapiro M., Struppa D.C., “On Clifford Analysis for Holomorphic Mappings”, Adv. Geom., 14:3 (2014), 413–426  crossref  mathscinet  zmath  isi  scopus
    2. Yu. Grigor'ev, “Three-dimensional analogue of Kolosov–Muskhelishvili formulae”, Modern Trends in Hypercomplex Analysis, Trends in Mathematics, eds. S. Bernstein, U. Kahler, I. Sabadini, F. Sommen, Birkhauser Boston, 2016, 203–215  crossref  mathscinet  isi
    3. B. B. Delgado, R. Michael Porter, “General solution of the inhomogeneous div-curl system and consequences”, Adv. Appl. Clifford Algebr., 27:4 (2017), 3015–3037  crossref  mathscinet  zmath  isi  scopus
    4. J. Bory Reyes, R. Abreu Blaya, M. A. Perez-de la Rosa, B. Schneider, “A quaternionic treatment of inhomogeneous Cauchy–Riemann type systems in some traditional theories”, Complex Anal. Oper. Theory, 11:5, SI (2017), 1017–1034  crossref  mathscinet  zmath  isi  scopus
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