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A supplementary proof of L p –logarithmic Sobolev inequality
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 1, pp. 119-132.

Dans cet article, nous complétons la preuve de l’inégalité de Sobolev logarithmique L p obtenue par Gentil dans [8] et donnons aussi une preuve supplémentaire. Notre approche est basée sur une équation de Hamilton–Jacobi et sur plusieurs approximations de fonctions dans W 1,p (ℝ n ).

In this paper, we bridge a gap in the proof of the L p –logarithmic Sobolev inequality obtained by Gentil [8, Theorem 1.1], and provide a supplementary proof. Our proof is based on a Hamilton–Jacobi equation and several approximations of functions in W 1,p (ℝ n ).

@article{AFST_2015_6_24_1_119_0,
     author = {Yasuhiro Fujita},
     title = {A supplementary proof of $L^p${\textendash}logarithmic {Sobolev} inequality},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {119--132},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 24},
     number = {1},
     year = {2015},
     doi = {10.5802/afst.1444},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1444/}
}
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Yasuhiro Fujita. A supplementary proof of $L^p$–logarithmic Sobolev inequality. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 1, pp. 119-132. doi : 10.5802/afst.1444. https://afst.centre-mersenne.org/articles/10.5802/afst.1444/

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