$L\sp q$-functional inequalities and weighted porous media equations

Jean Dolbeault, Ivan Gentil, Arnaud Guillin & Feng-Yu Wang
Using measure-capacity inequalities we study new functional inequalities, namely Lq- Poincaré inequalities and Lq-logarithmic Sobolev inequalities for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to a so-called weighted porous media equation in terms of L2-norms and entropies.
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