Lq-functional inequalities and weighted porous media equations
classification
🧮 math.AP
keywords
inequalitiesmediaporousweightedasymptoticbehaviorconsequenceentropies
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Using measure-capacity inequalities we study new functional inequalities, namely L^q-Poincar\'{e} 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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