Lq-functional inequalities and weighted porous media equations
Jean Dolbeault, Ivan Gentil, Arnaud Guillin, Feng-Yu Wang
Abstract
Using measure-capacity inequalities we study new functional inequalities, namely Lq-Poincaré inequalities and Lq-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 L2-norms and entropies.
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