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Laplacian decomposition of vector fields on fractal surfaces

✍ Scribed by R. Abreu-Blaya; J. Bory-Reyes; T. Moreno-García; D. Peña-Peña

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
99 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In the present paper we consider domains in ℝ^3^ 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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