Lq-functional inequalities and weighted porous media equations

Abstract

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.