A new multicomponent Poincaré-Beckner inequality
arXiv:1603.06493 · doi:10.1016/j.jfa.2016.12.018
Abstract
We prove a new vectorial functional inequality of Poincaré-Beckner type. The inequality may be interpreted as an entropy-entropy production one for a gradient flow in the metric space of Radon measures. The proof uses subtle analysis of combinations of related super- and sub-level sets employing the coarea formula and the relative isoperimetric inequality.
Introduction added, some cosmetical issues fixed
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