Laplacian decomposition of vector fields on fractal surfaces

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

doi:10.1002/mma.952

Laplacian decomposition of vector fields on fractal surfaces

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

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	849-857
Number of pages	9
Journal	Mathematical Methods in the Applied Sciences
Volume	31
Issue number	7
DOIs	https://doi.org/10.1002/mma.952
State	Published - 10 May 2008
Externally published	Yes

Keywords

Fractals
Quatemionic analysis
Vector fields

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10.1002/mma.952

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title = "Laplacian decomposition of vector fields on fractal surfaces",

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.",

keywords = "Fractals, Quatemionic analysis, Vector fields",

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AU - Abreu-Blaya, R.

AU - Bory-Reyes, J.

AU - Moreno-García, T.

AU - Peña-Peña, D.

PY - 2008/5/10

Y1 - 2008/5/10

N2 - 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.

AB - 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.

KW - Fractals

KW - Quatemionic analysis

KW - Vector fields

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U2 - 10.1002/mma.952

DO - 10.1002/mma.952

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 7

ER -

Laplacian decomposition of vector fields on fractal surfaces

Abstract

Keywords

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