\(L^q\)-functional inequalities and weighted porous media equations

DOI10.1007/s11118-007-9066-0zbMath1148.26018arXivmath/0701037OpenAlexW2128097535MaRDI QIDQ2471750

Jean Dolbeault, Feng-Yu Wang, Ivan Gentil, Arnaud Guillin

Publication date: 18 February 2008

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701037

zbMATH Keywords

Poincaré inequalityVarianceAsymptotic behaviourEntropyRate of convergenceLogarithmic Sobolev inequalityNonlinear parabolic equationsWeighted Sobolev spacesLarge time asymptoticsPorous media equation

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Nonlinear parabolic equations (35K55) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functional inequalities, including subadditivity, convexity, etc. (39B62) Spaces of measures (46E27) Inequalities involving derivatives and differential and integral operators (26D10)

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Smoothing effects for the filtration equation with different powers ⋮ Trends to equilibrium in total variation distance ⋮ Fractional porous media equations: existence and uniqueness of weak solutions with measure data ⋮ A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling ⋮ Global renormalised solutions and equilibration of reaction-diffusion systems with nonlinear diffusion ⋮ Symmetrization inequalities for probability metric spaces with convex isoperimetric profile ⋮ Variational principle for weighted porous media equation ⋮ Generalized stochastic flows and applications to incompressible viscous fluids ⋮ Convex Sobolev inequalities derived from entropy dissipation ⋮ Weighted fast diffusion equations II: sharp asymptotic rates of convergence in relative error by entropy methods ⋮ Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities ⋮ Slow decay of Gibbs measures with heavy tails ⋮ Convex Sobolev inequalities related to unbalanced optimal transport ⋮ Conditions at infinity for the inhomogeneous filtration equation

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