[Diffusions non linéaires et constantes optimales dans des inégalités de type Sobolev : comportement asymptotique d'équations faisant intervenir le p-Laplacien]
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.
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.
Accepté le :
Publié le :
Manuel Del Pino 1 ; Jean Dolbeault 2
@article{CRMATH_2002__334_5_365_0,
author = {Manuel Del Pino and Jean Dolbeault},
title = {Nonlinear diffusions and optimal constants in {Sobolev} type inequalities: asymptotic behaviour of equations involving the $ \mathbf{p}${-Laplacian}},
journal = {Comptes Rendus. Math\'ematique},
pages = {365--370},
publisher = {Elsevier},
volume = {334},
number = {5},
year = {2002},
doi = {10.1016/S1631-073X(02)02225-2},
language = {en},
}
TY - JOUR
AU - Manuel Del Pino
AU - Jean Dolbeault
TI - Nonlinear diffusions and optimal constants in Sobolev type inequalities: asymptotic behaviour of equations involving the $ \mathbf{p}$-Laplacian
JO - Comptes Rendus. Mathématique
PY - 2002
SP - 365
EP - 370
VL - 334
IS - 5
PB - Elsevier
DO - 10.1016/S1631-073X(02)02225-2
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ID - CRMATH_2002__334_5_365_0
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%P 365-370
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Manuel Del Pino; Jean Dolbeault. Nonlinear diffusions and optimal constants in Sobolev type inequalities: asymptotic behaviour of equations involving the $ \mathbf{p}$-Laplacian. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 365-370. doi : 10.1016/S1631-073X(02)02225-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02225-2/
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