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Lq-functional inequalities and weighted porous media equations

Jean Dolbeault·Ivan Gentil·Arnaud Guillin·Feng-Yu Wang
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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.

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Jean Dolbeault, Ivan Gentil, Arnaud Guillin, Feng-Yu Wang. 2007-01-01. Lq-functional inequalities and weighted porous media equations. https://arxiv.org/abs/math/0701037

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