Lq-functional inequalities and weighted porous media equations

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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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Analysis of PDEs, 26D10;35K55;39B62;46E27;46E35;60E15

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http://salesiana.dossiersoluciones.com/handle/123456789/120956

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701037
 http://arxiv.org/abs/math/0701037

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arXiv