Abstract
AbstractIn the present paper we consider domains in ℝ3 with fractal boundaries. Our main purpose is to study the boundary values of Laplacian vector fields, paying special attention to the problem of decomposing a Hölder continuous vector field on the boundary of a domain as a sum of two Hölder continuous vector fields which are Laplacian in the domain and in the complement of its closure, respectively. Our proofs are based on the intimate relationships between the theory of Laplacian vector fields and quaternionic analysis. Copyright © 2007 John Wiley & Sons, Ltd.
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