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Research Article | Open Access

The Helmholtz decomposition of vector fields for two-dimensional exterior Lipschitz domains

School of General and Management Studies, Suwa University of Science, 5000-1, Toyohira, Chino, Nagano 391-0292, Japan
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Abstract

Let Ω be an exterior Lipschitz domain in R 2 . It is proved that the Helmholtz decomposition of the vector fields in L p ( Ω ; R 2 ) exists if p satisfies | 1 / p − 1 / 2 | < 1 / 4 + ε with some constant ε = ε ( Ω ) ∈ ( 0 , 1 / 4 ], where it is allowed to take ε = 1 / 4 if ∂ Ω ∈ C 1 .

Keywords

exterior Lipschitz domainsHelmholtz decomposition
CLC number: 35J57, 35Q35

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17886-17900
DOI: 10.3934/math.2024870

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Watanabe K. The Helmholtz decomposition of vector fields for two-dimensional exterior Lipschitz domains. AIMS Mathematics, 2024, 9(7): 17886-17900. https://doi.org/10.3934/math.2024870

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Received: 27 March 2024
Revised: 08 May 2024
Accepted: 21 May 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)