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Nonlinear diffusions and optimal constants in Sobolev type inequalities: asymptotic behaviour of equations involving the p-Laplacian

Del Pino, Manuel; Dolbeault, Jean (2002), Nonlinear diffusions and optimal constants in Sobolev type inequalities: asymptotic behaviour of equations involving the p-Laplacian, Comptes rendus mathématique, 334, 5, p. 365-370. http://dx.doi.org/10.1016/S1631-073X(02)02225-2

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Type
Article accepté pour publication ou publié
Date
2002
Journal name
Comptes rendus mathématique
Volume
334
Number
5
Publisher
Elsevier
Pages
365-370
Publication identifier
http://dx.doi.org/10.1016/S1631-073X(02)02225-2
Metadata
Show full item record
Author(s)
Del Pino, Manuel
Dolbeault, Jean cc
Abstract (FR)
Nous étudions le comportement asymptotique des solutions positives ou nulles de : ut=Δpum à l'aide d'une estimation d'entropie qui repose sur l'utilisation d'une sous-famille des inégalités de Gagliardo–Nirenberg – ou, dans le cas limite m=(p−1)−1, d'une inégalité de Sobolev logarithmique dans W1,p – pour laquelle on connait des fonctions optimales.
Abstract (EN)
We study the asymptotic behaviour of nonnegative solutions to: ut=Δpum using an entropy estimate based on a sub-family of the Gagliardo–Nirenberg inequalities – or, in the limit case m=(p−1)−1, on a logarithmic Sobolev inequality in W1,p – for which optimal functions are known.
Subjects / Keywords
Gagliardo–Nirenberg inequalities; Sobolev type inequalities

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