Calculus of Variations and Geometric Measure Theory
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D. Tewodrose

Weighted Sobolev inequalities in CD(0,N) spaces

created by tewodrose on 22 Nov 2016
modified on 19 Nov 2020


Accepted Paper

Inserted: 22 nov 2016
Last Updated: 19 nov 2020

Journal: ESAIM: COCV
Year: 2018


In this note, we prove global weighted Sobolev inequalities on non-compact CD(0,N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result due to Minerbe stated for Riemannian manifolds with non-negative Ricci curvature and a suitable reverse doubling condition. We use this result in the context of RCD(0,N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.


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