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arXiv · 2301.02701

The Helmholtz decomposition of a $BMO$ type vector field in a slightly perturbed half space

Yoshikazu Giga·Zhongyang Gu
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Abstract

We introduce a space of $L^2$ vector fields with bounded mean oscillation whose normal component to the boundary is well-controlled. We establish its Helmholtz decomposition in the case when the domain is a perturbed $C^3$ half space in $\mathbf{R}^n$ $(n \geq 3)$ with small perturbation.

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Yoshikazu Giga, Zhongyang Gu. 2023-01-06. The Helmholtz decomposition of a $BMO$ type vector field in a slightly perturbed half space. https://doi.org/10.1007/s00021-023-00781-z

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