Emmanuel Russ
A note on precised Hardy inequalities on Carnot groups and Riemannian manifolds.
Mon, 03/29/2010 - 15:01 — SomNambulAuthors: Yannick Sire, Emmanuel Russ
Subjects: Functional Analysis
AbstractWe prove non local Hardy inequalities on Carnot groups and Riemannian
manifolds, relying on integral representations of fractional Sobolev norms.Non local Poincar\'e inequalities on Lie groups with polynomial volume growth.
Mon, 01/25/2010 - 16:01 — SomNambulAuthors: Yannick Sire, Emmanuel Russ
Subjects: Functional Analysis
AbstractLet $G$ be a real connected Lie group with polynomial volume growth, endowed
with its Haar measure $dx$. Given a $C^2$ positive function $M$ on $G$, we give
a sufficient condition for an $L^2$ Poincar\'e inequality with respect to the
measure $M(x)dx$ to hold on $G$. We then establish a non-local Poincar\'e
inequality on $G$ with respect to $M(x)dx$.Fractional Poincar\'e inequalities for general measures.
Wed, 11/25/2009 - 16:01 — SomNambulAuthors: Clément Mouhot, Yannick Sire, Emmanuel Russ
Subjects: Analysis of PDEs
AbstractWe prove a fractional version of Poincar\'e inequalities in the context of
$\R^n$ endowed with a fairly general measure. Namely we prove a control of an
$L^2$ norm by a non local quantity, which plays the role of the gradient in the
standard Poincar\'e inequality. The assumption on the measure is the fact that
it satisfies the classical Poincar\'e inequality, so that our result is an
improvement of the latter inequality. Moreover we also quantify the tightness
at infinity provided by the control on the fractional derivative in terms of a
weight growing at infinity.
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