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The optimal Euclidean L-Sobolev logarithmic inequality |
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| Authors: | Manuel Del Pino Jean Dolbeault |
| Affiliation: | a Dept de Ingenieria Mathematica & C.M.M. (UMR CNRS No. 2071), F.C.F.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile b Ceremade (UMR CNRS No. 7534), Université Paris IX-Dauphine, Place de Lattre de Tassigny, 75775 Paris Cédex 16, France |
| Abstract: | We prove an optimal logarithmic Sobolev inequality in  . Explicit minimizers are given. This result is connected with best constants of a special class of Gagliardo-Nirenberg-type inequalities. |
| Keywords: | primary 35J85 secondary 35J20 49J40 35A05 46E35 49K30 |
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