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Entropy flux - electrostatic capacity - graphical mass


Author: J. Xiao
Journal: Proc. Amer. Math. Soc. 145 (2017), 825-832
MSC (2010): Primary 31B15, 35N25, 52A40
DOI: https://doi.org/10.1090/proc/13259
Published electronically: August 5, 2016
MathSciNet review: 3577881
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Abstract: This note shows that the optimal inequality

$\displaystyle \mathsf {F}(K,\kappa )\le \mathsf {C}(K)\le 2(n-2)\sigma _{n-1}\mathsf {M}(\mathbb{R}^n\setminus K^\circ ,\delta +df\otimes df) $

holds for the entropy flux $ \mathsf {F}(K,\kappa )$, the electrostatic capacity $ \mathsf {C}(K)=\mathsf {C}(\partial K)$ and the graphical mass $ \mathsf {M}(\mathbb{R}^n\setminus K^\circ ,\delta +df\otimes df)$ generated by a compact $ K\subset \mathbb{R}^{n\ge 3}$ with nonempty interior $ K^\circ $ and smooth boundary $ \partial K$.

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Additional Information

J. Xiao
Affiliation: Department of Mathematics and Statistics, Memorial University, St. John’s, Newfoundland A1C 5S7, Canada
Email: jxiao@mun.ca

DOI: https://doi.org/10.1090/proc/13259
Received by editor(s): October 20, 2015
Received by editor(s) in revised form: April 22, 2016
Published electronically: August 5, 2016
Additional Notes: This project was in part supported by NSERC of Canada (202979463102000).
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society