TY - JOUR
T1 - A quaternionic treatment of the inhomogeneous div-rot system
AU - Colombo, F.
AU - Luna-Elizarrarás, M. E.
AU - Sabadini, I.
AU - Shapiro, M.
AU - Struppa, D. C.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Algebraic analysis
KW - Cohomology vanishing
KW - Div-rot system
KW - Right inverse operator
UR - http://www.scopus.com/inward/record.url?scp=84855881381&partnerID=8YFLogxK
U2 - 10.17323/1609-4514-2012-12-1-37-48
DO - 10.17323/1609-4514-2012-12-1-37-48
M3 - Artículo
SN - 1609-3321
VL - 12
SP - 37
EP - 48
JO - Moscow Mathematical Journal
JF - Moscow Mathematical Journal
IS - 1
ER -