LOGARITHMIC SOBOLEV INEQUALITIES: CONDITIONS AND COUNTEREXAMPLES

By Feng-Yu Wang. 2001

69 citations recorded by the source corpus.

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Citations in the corpus

Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below (2006, background): “This inequality has been applied and further developed to the study of functional inequalities (see [1,22,27,29]), heat kernel estimates (see [4,10]), higher order eigenvalues (see [11,28,30]), transportation cost inequalities (see [5]), and short time behavior of transition probabilities (see [2,3,”
On quadratic transportation cost inequalities (2006, background): “The latter restriction is very important and has to be compared with Wang’s results ([24] and [25]) telling that a logarithmic-Sobolev inequality holds provided the curvature assumption above and the integrability condition (EIε(2)) in Theorem 1.”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, methodology): “18 (Wang [64, 66]).”
FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES (2000, methodology): “just consider f with kfkp = 1 instead of kfk2 = 1, and apply the Harnack inequality in Theorem 5.5 for big p, see [ 61 ] for details.”
Functional Inequalities for Empty Essential Spectrum (2000, methodology): “Remark. According to Croke’s isoperimetric inequality [14], when @M = ;, (2.6) holds for W = 0 and p = d provided either i(M) = 1 or i(M) > 0 and the Ricci curvature is bounded from below, where i(M) denotes the injectivity radius of M. Here, we present below a result based on a result due to [ 36 ]”
Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound (2009, methodology): “Moreover, it follows from [48] that 1/2 is an upper bound on the value of δ in any possible counter example as above (this will be described in more detail below).”
Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition (2011, background): “[75, 16, 8, 9, 58]) considered an integrability condition of the form ∫”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, background): “[34, 36, 29, 30] for applications to functional inequalities; [1, 2, 17] for the study of short time behavior of infinite-dimensional ∗Supported in part by the DFG through the Internationales Graduiertenkolleg “Stochastics and Real World Models”, the SFB 701 and NNSFC(10721091).”
Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds (2003, background): “See for example [2, 4, 5, 10, 12, 13, 14, 23, 25, 33, 36] and references therein.”