### Analysis Seminar

Thursday, September 28, 2017 - 3:00pm

#### Francis Seuffert

Penn

Location

University of Pennsylvania

DRL 4C8

The Bianchi-Egnell Stability Estimate is a stability estimate or quantitative version of the Sobolev Inequality – it states that the difference of terms in the Sobolev Inequality controls the distance of a given function from the manifold of extremals of the Sobolev Inequality with distance measured in the gradient square or $\dot{H}^1$ norm. In this talk, we present an extension of the Bianchi-Egnell Stability Estimate to Bakry, Gentil, and Ledoux’s Generalization of the Sobolev Inequality to Continuous Dimensions. We also demonstrate a deep link between the Sobolev Inequality and a one-parameter family of sharp Gagliardo-Nirenberg-Sobolev (GNS) inequalities and how this link can be used to derive a new stability estimate on the one-parameter family of sharp GNS inequalities from our stability estimate on Bakry, Gentil, and Ledoux’s Generalization of the Sobolev Inequality to Continuous Dimensions