Hardy-type inequalities for vector fields with vanishing tangential components
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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.References
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Additional Information
- Xingfei Xiang
- Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
- Email: xiangxingfei@126.com
- Zhibing Zhang
- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
- Email: zhibingzhang29@126.com
- Received by editor(s): March 24, 2014
- Received by editor(s) in revised form: September 2, 2014, and October 31, 2014
- Published electronically: January 23, 2015
- Communicated by: Jeremy Tyson
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5369-5379
- MSC (2010): Primary 26D10, 42B20, 46E40
- DOI: https://doi.org/10.1090/S0002-9939-2015-12668-8
- MathSciNet review: 3411152