Generalizations of logarithmic Sobolev inequalities

DOI10.3934/dcdss.2008.1.329zbMath1152.35326OpenAlexW1972239922MaRDI QIDQ947035

Jochen Merker

Publication date: 29 September 2008

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2008.1.329

zbMATH Keywords

ultracontractivitydoubly nonlinear \(p\)-Laplacianlogarithmic Gagliardo-Nirenberg inequalities

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

Related Items (12)

Shannon's inequality for the Rényi entropy and an application to the uncertainty principle ⋮ Several logarithmic Caffarelli-Kohn-Nirenberg inequalities and applications ⋮ Non-blow-up and blow-up results to heat equations with logarithmic nonlinearity on stratified groups ⋮ Existence of weak solutions to doubly degenerate diffusion equations. ⋮ Strengthened fractional Sobolev type inequalities in Besov spaces ⋮ Anisotropic Shannon inequality ⋮ Fractional Hardy-Sobolev inequalities and existence results for fractional sub-Laplacians ⋮ Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle ⋮ Unnamed Item ⋮ Rearrangement and the weighted logarithmic Sobolev inequality ⋮ Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms ⋮ Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

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