nash inequality
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scholarly journals Weighted Sobolev Inequalities in CD(0,N) spaces

2020 ◽  
Author(s):  
David Tewodrose
Keyword(s):  
Heat Kernel ◽  
Growth Condition ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Sobolev Inequalities ◽  
Uniform Bound ◽  
Nash Inequality ◽  
Weighted Sobolev Inequalities

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 from Minerbe stated for Riemannian manifolds with non-negative Ricci curvature. 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.

scholarly journals A dual form of the sharp Nash inequality and its weighted generalization

2018 ◽  
Vol 51 (1) ◽  
pp. 129-144
Author(s):  
Eric A. Carlen ◽  
Elliott H. Lieb
Keyword(s):  
Nash Inequality ◽  
Dual Form

scholarly journals Spectral condition, hitting times and Nash inequality

2014 ◽  
Vol 50 (4) ◽  
pp. 1213-1230 ◽  
Author(s):  
Eva Löcherbach ◽  
Oleg Loukianov ◽  
Dasha Loukianova
Keyword(s):  
Hitting Times ◽  
Spectral Condition ◽  
Nash Inequality

scholarly journals THE BEST-CONSTANT PROBLEM FOR A FAMILY OF GAGLIARDO–NIRENBERG INEQUALITIES ON A COMPACT RIEMANNIAN MANIFOLD

2003 ◽  
Vol 46 (1) ◽  
pp. 117-146 ◽  
Author(s):  
Christophe Brouttelande
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Logarithmic Sobolev Inequality ◽  
Sobolev Inequalities ◽  
Best Constant ◽  
Nash Inequality ◽  
Primary 58J05 ◽  
Compact Case ◽  
Limiting Case

AbstractThe best-constant problem for Nash and Sobolev inequalities on Riemannian manifolds has been intensively studied in the last few decades, especially in the compact case. We treat this problem here for a more general family of Gagliardo–Nirenberg inequalities including the Nash inequality and the limiting case of a particular logarithmic Sobolev inequality. From the latter, we deduce a sharp heat-kernel upper bound.AMS 2000 Mathematics subject classification: Primary 58J05

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