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Convex Sobolev inequalities and spectral gap by Jean-Philippe Bartier; Jean Dolbeault is a Mathematics article available to read on EtoBox.
What is Convex Sobolev inequalities and spectral gap about?
This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities.
Who reads Convex Sobolev inequalities and spectral gap?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Jean-Philippe Bartier; Jean Dolbeault
- Publisher
- Elsevier Science; Elsevier ; Elsevier Masson; Elsevier BV; Cellule MathDoc/CEDRAM (ISSN 1631-073X)
- Published
- 2006
- Language
- FR
- Field
- Mathematics (Physical Sciences)