Displaying similar documents to “Une condition asymptotique pour le calcul de constantes de Sobolev logarithmiques sur la droite”

Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?

Laurent Miclo (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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Classically, Hardy’s inequality enables to estimate the spectral gap of a one-dimensional diffusion up to a factor belonging to [ 1 , 4 ] . The goal of this paper is to better understand the latter factor, at least in a symmetric setting. In particular, we will give an asymptotical criterion implying that its value is exactly 4. The underlying argument is based on a semi-explicit functional for the spectral gap, which is monotone in some rearrangement of the data. To find it will resort to some...