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The optimal Euclidean Lp-Sobolev logarithmic inequality

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
Journal name
Journal of Functional Analysis
Volume
197
Number
1
Publisher
Elsevier
Pages
151-161
Publication identifier
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Author(s)
Del Pino, Manuel
Dolbeault, Jean cc
Abstract (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.
Subjects / Keywords
Gagliardo–Nirenberg inequalities; Logarithmic Sobolev inequality; Optimal constants; Minimizers; Orlicz spaces