Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces

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Abstract

In this paper we consider Jordan domains in real Euclidean spaces of higher dimension which have fractal boundaries. The case of decomposing a Hölder continuous multivector field on the boundary of such domains is obtained in closed form as sum of two Hölder continuous multivector fields harmonically extendable to the domain and to the complement of its closure respectively. The problem is studied making use of the Teodorescu transform and suitable extension of the multivector fields. Finally we establish equivalent condition on a Hölder continuous multivector field on the boundary to be the trace of a harmonic Hölder continuous multivector field on the domain.