Hardy-type inequalities for vector fields with vanishing tangential components

Xiang, Xingfei; Zhang, Zhibing

doi:10.1090/S0002-9939-2015-12668-8

Hardy-type inequalities for vector fields with vanishing tangential components
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Proc. Amer. Math. Soc. 143 (2015), 5369-5379 Request permission

Abstract:

This note studies Hardy-type inequalities for vector fields with the $L^1$ norm of the operator $\operatorname {curl}$. In contrast to the well-known results in the whole space for the divergence-free vector fields, we generalize the Hardy-type inequalities to bounded domains and to non-divergence-free vector fields with tangential components vanishing on the boundary.

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