Refined convex Sobolev inequalities

Arnold, Anton; Dolbeault, Jean

Arnold, Anton; Dolbeault, Jean (2005), Refined convex Sobolev inequalities, Journal of Functional Analysis, 225, 2, p. 337-351. http://dx.doi.org/10.1016/j.jfa.2005.05.003

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Type

Article accepté pour publication ou publié

Date

2005

Journal name

Journal of Functional Analysis

Volume

225

Number

Publisher

Elsevier

Pages

337-351

Abstract (EN)

This paper is devoted to refinements of convex Sobolev inequalities in the case of power law relative entropies: a nonlinear entropy–entropy production relation improves the known inequalities of this type. The corresponding generalized Poincaré-type inequalities with weights are derived. Optimal constants are compared to the usual Poincaré constant.

Subjects / Keywords

Sobolev inequality; Poincaré inequality; Entropy method; Diffusion; Logarithmic Sobolev inequality; Spectral gap