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arXiv · 2405.05228

Generalized vector potential and Trace Theorem for Lipschitz domains

Zhen Liu·Jinbiao Wu
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Abstract

The vector potential is a fundamental concept widely applied across various fields. This paper presents an existence theorem of a vector potential for divergence-free functions in $W^{m,p}(\mathbb{R}^N,\mathbb{T})$ with general $m,p,N$. Based on this theorem, one can establish the space decomposition theorem for functions in $W^{m,p}_0(\operatorname{curl};\Omega,\mathbb{R}^N)$ and the trace theorem for functions in $W^{m,p}(\Omega)$ within the Lipschitz domain $\Omega \subset \mathbb{R}^N$. The methods of proof employed in this paper are straightforward, natural, and consistent.

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Zhen Liu, Jinbiao Wu. 2024-05-08. Generalized vector potential and Trace Theorem for Lipschitz domains. https://arxiv.org/abs/2405.05228

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