Summary: Refined Convex Sobolev Inequalities
Anton ARNOLD 1
and Jean DOLBEAULT 2
1
Institut f¨ur Numerische und Angewandte Mathematik, Universit¨at M¨unster
Einsteinstr. 62, D-48149 M¨unster, Germany
E-mail: anton.arnold@math.uni-muenster.de
2
CEREMADE, U.M.R. C.N.R.S. no. 7534, Universit´e Paris IX-Dauphine
Pl. du Mar´echal de Lattre de Tassigny, 75775 Paris C´edex 16, France
E-mail: dolbeaul@ceremade.dauphine.fr
April 28, 2005
Abstract
This paper is devoted to refinements of convex Sobolev inequalities in the case of
power law relative entropies: a nonlinear entropy­entropy production relation im-
proves the known inequalities of this type. The corresponding generalized Poincar´e
type inequalities with weights are derived. Optimal constants are compared to the
usual Poincar´e constant.
Key words and phrases: Sobolev inequality ­ Poincar´e inequality ­ entropy method
­ diffusion ­ logarithmic Sobolev inequality ­ spectral gap

Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien

Collections: Mathematics