Lq-functional inequalities and weighted porous media equations

2007/01/01 by Jean Dolbeault, Dolbeault, Jean, Ivan Gentil +5 · 1 citation
Mathematics · #26D10 #35K55 #39B62 #46E27 #46E35 #60E15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0701037

openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²-norms and entropies.

Citations

• Logarithmic Sobolev Inequalities

Cited by

• On the Bakry-Emery criterion for linear diffusions and weighted porous media equations

Related

• Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities
• Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities
• Well-posedness and L¹-L^p Smoothing Effect of the Porous Media Equation under Poincaré Inequality
• Sharp short and long time \mathbf L^{\boldsymbol ∞} bounds for solutions to porous media equations with Neumann boundary conditions
• On the Bakry-Emery criterion for linear diffusions and weighted porous media equations