L-functional inequalities and weighted porous media equations
نویسندگان
چکیده
Using measure-capacity inequalities we study new functional inequalities, namely LPoincaré inequalities Varμ(f) 1/q ≤ CP ∫ |∇f | dν and L-logarithmic Sobolev inequalities Entμ ( f )1/q ≤ CLS ∫ |∇f | dν for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media equation ∂u ∂t = ∆u −∇ψ · ∇u for m ≥ 1, in terms of L-norms and entropies. Mathematics Subject Classification 2000: 26D10; 35K55, 39B62, 46E27, 46E35, 60E15
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تاریخ انتشار 2007