论文标题
关于局部对数Sobolev不平等的变异解释
On the variational interpretation of local logarithmic Sobolev inequalities
论文作者
论文摘要
著名的奥托微积分已确立自己的强大工具，用于证明定量的耗散估计值，并提供了对某些功能不平等的优雅几何解释，例如对数Sobolev不平等。但是，这种不平等的\ emph {local}版本，可以通过巴克里 - emery-ledoux $γ$ -calculus证明，尚未根据这种riemannian形式主义来解释。在此简短的说明中，我们通过解释Otto计算如何应用于Schr {Ö} Dinger问题如何产生对局部对数Sobolev不平等的变化解释，从而可以解释新的局部不平等类别。
The celebrated Otto calculus has established itself as a powerful tool for proving quantitative energy dissipation estimates and provides with an elegant geometric interpretation of certain functional inequalities such as the Logarithmic Sobolev inequality. However, the \emph{local} versions of such inequalities, which can be proven by means of Bakry-Emery-Ledoux $Γ$-calculus, has not yet been given an interpretation in terms of this Riemannian formalism. In this short note we close this gap by explaining how Otto calculus applied to the Schr{ö}dinger problem yields a variations interpretation of the local logarithmic Sobolev inequalities, that could possibly unlock novel class of local inequalities.
