The optimal Euclidean Lp-Sobolev logarithmic inequality

Del Pino, Manuel; Dolbeault, Jean

Del Pino, Manuel; Dolbeault, Jean (2003), The optimal Euclidean Lp-Sobolev logarithmic inequality, Journal of Functional Analysis, 197, 1, p. 151-161. http://dx.doi.org/10.1016/S0022-1236(02)00070-8

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Type

Article accepté pour publication ou publié

Date

2003

Nom de la revue

Journal of Functional Analysis

Volume

197

Numéro

Éditeur

Elsevier

Pages

151-161

Résumé (EN)

We prove an optimal logarithmic Sobolev inequality in Wl,p(Rd). Explicit minimizers are given. This result is connected with best constants of a special class of Gagliardo–Nirenberg-type inequalities.

Mots-clés

Gagliardo–Nirenberg inequalities; Logarithmic Sobolev inequality; Optimal constants; Minimizers; Orlicz spaces