Laplacian decomposition of vector fields on fractal surfaces

R. Abreu-Blaya, J. Bory-Reyes, T. Moreno-García, D. Peña-Peña

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Abstract

In 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 Holder continuous vector field on the boundary of a domain as a sum of two Holder 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 quatemionic analysis. Copyright © 2007 John Wiley & Sons, Ltd.
Original languageAmerican English
Pages (from-to)849-857
Number of pages763
JournalMathematical Methods in the Applied Sciences
DOIs
StatePublished - 10 May 2008
Externally publishedYes

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