First order differential operators associated to Δ˜=div(B∇) operator in Clifford analysis

Let ℱ be a given differential operator acting with respect to spacelike variables, then a function space ℬ is called an associated space to ℱ if ℱ applies ℬ into itself. In this research work, a characterization of all the first-order differential operators with coefficients in the Clifford algebra...

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Published in:AIP Conference Proceedings 2024-01, Vol.2994 (1)
Main Authors: Vanegas, Carmen Judith, Jimenez, Franklin Vargas
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Language:English
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Boundary value problems
Function space
Mathematical analysis
Operators (mathematics)
Partial differential equations
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description Let ℱ be a given differential operator acting with respect to spacelike variables, then a function space ℬ is called an associated space to ℱ if ℱ applies ℬ into itself. In this research work, a characterization of all the first-order differential operators with coefficients in the Clifford algebra CLn that are associated to the space of solution functions of the partial differential equation Δ˜=div(B∇) u = 0 has been determined. To make this possible the equation Δ˜u=0 and some special solutions of such equation were used. The results found imply that the technique of associated spaces allows to solve certain initial value problems.
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subjects Boundary value problems
Function space
Mathematical analysis
Operators (mathematics)
Partial differential equations
title First order differential operators associated to Δ˜=div(B∇) operator in Clifford analysis
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