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First order differential operators associated to Δ = d i v (B ∇) operator in Clifford analysis

Abstract:

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 Δu=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.