L^q-functional inequalities and weighted porous media equations.

Dolbeault, Jean; Gentil, Ivan; Guillin, Arnaud; Wang, Feng-Yu

Dolbeault, Jean; Gentil, Ivan; Guillin, Arnaud; Wang, Feng-Yu (2008), L^q-functional inequalities and weighted porous media equations., Potential Analysis, 28, 1, p. 35-39. http://dx.doi.org/10.1007/s11118-007-9066-0

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00122415

Date

2008

Journal name

Potential Analysis

Volume

Number

Publisher

Springer

Pages

35-39

Abstract (EN)

Using measure-capacity inequalities we study new functional inequalities, namely L^q-Poincaré inequalities and L^q-logarithmic Sobolev inequalities. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media equation for m?1, in terms of L^2-norms and entropies.

Subjects / Keywords

Equations aux dérivées partielles; Analysis