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arXiv · 2011.12029

Normal trace for vector fields of bounded mean oscillation

Yoshikazu Giga·Zhongyang Gu
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Abstract

We introduce various spaces of vector fields of bounded mean oscillation ($BMO$) defined in a domain so that normal trace on the boundary is bounded when its divergence is well controlled. The behavior of "normal" component and "tangential" component may be different for our $BMO$ vector fields. As a result zero extension of the normal component stays in $BMO$ although such property may not hold for tangential components.

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Yoshikazu Giga, Zhongyang Gu. 2020-11-24. Normal trace for vector fields of bounded mean oscillation. https://arxiv.org/abs/2011.12029

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