Weighted sobolev inequalities in CD(0, n) spaces

David Tewodrose

doi:10.1051/cocv/2020080

Weighted sobolev inequalities in CD(0, n) spaces

David Tewodrose

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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 [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] 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.

Originele taal-2	English
Artikelnummer	2020080
Aantal pagina's	19
Tijdschrift	ESAIM - Control, Optimisation and Calculus of Variations
Volume	27
DOI's	https://doi.org/10.1051/cocv/2020080
Status	Published - 2021

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© The authors. Published by EDP Sciences, SMAI 2021.

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year = "2021",

doi = "10.1051/cocv/2020080",

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N1 - Publisher Copyright: © The authors. Published by EDP Sciences, SMAI 2021.

PY - 2021

Y1 - 2021

N2 - 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 [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] 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.

AB - 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 [V. Minerbe, G.A.F.A. 18 (2009) 1696-1749] 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.

KW - Heat kernel

KW - Metric measure spaces#curvature-dimension conditions

KW - Sobolev inequalities

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DO - 10.1051/cocv/2020080

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JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 2020080

ER -

Weighted sobolev inequalities in CD(0, n) spaces

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