Hypercontractivity of Hamilton-Jacobi equations

By Sergey G. Bobkov, Ivan Gentil, Michel Ledoux. 2001

357 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b46d2f1fdbaad4985c93a77ae6007e16a33e47ec

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In Applied Mathematics

Citations in the corpus

Modified logarithmic Sobolev inequalities and transportation inequalities (2004, methodology): “However we show here, that once this result assumed, the methodology presented in Bobkov-Gentil-Ledoux [ BGL01 ], for the exponential measure, still works.”
A large deviation approach to some transportation cost inequalities (2005, background): “Ledoux [1], that if μ satisfies the logarithmic Sobolev inequality, then it also satisfies T2.”
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,”
Ricci curvature for metric-measure spaces via optimal transport (2004, background): “Again in the case of Riemannian manifolds, a further circle of ideas relates displacement convexity to log Sobolev inequalities, Poincaré inequalites, Talagrand inequalities and concentration of measure [7] [8] [25] [33].”
Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, neutral): “The advantage of this approach is that it avoids the assumption on curvature lower bounds used in previous articles (see [2, 3, 7, 15, 16]), which is very hard to verify in the framework of non-linear SPDEs.”
Convergence to equilibrium for granular media equations and their Euler schemes (2003, methodology): “At this point we make use of a result established by Otto and Villani in [9] and reformulated by Bobkov, Gentil and Ledoux [6].”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, neutral): “(1.1)”
Harnack inequalities on manifolds with boundary and applications (2009, methodology): “Note that this type inequality was used in [4] for the study of HWI inequalities on manifolds without boundary.”
Transportation-information inequalities for Markov processes (2007, background): “The reader is referred to the textbooks by Ledoux [27] and Villani [39, 38] for further references pertaining to this very active field.”
Transport Inequalities. A Survey (2010, background): “Soon after [89], Bobkov, Gentil and Ledoux have proposed in [16] a much more elementary proof relying on simple computations on the Hamilton-Jacobi semigroup.”
A Riemannian interpolation inequality à la Borell, Brascamp and Lieb (2001, background): “mentioned in [ 9 ] and [14], Maurey’s property (τ) and its generalization by Bobkov and Ledoux [8] can be extended to Riemannian manifolds whose Ricci curvature has a strictly positive lower bound to recover the Bakry‐ Emery [3] logarithmic Sobolev inequality, as well as transport and concentration ”
Hamilton–Jacobi semigroup on length spaces and applications (2006, methodology): “5, we can now use the strategy of [2] to prove Theorem 1.”
Characterization of Talagrand's like transportation-cost inequalities on the real line (2006, methodology): “The cases p = 1 and p = 2 were obtained by Talagrand in [18], the case p ∈ (1, 2) was treated by Gentil, Guillin and Miclo in [9] and the case p ≥ 2 by Bobkov and Ledoux in [4].”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, neutral): “Sobolev inequality [23, 6, 30], and that they imply a Poincaré, or spectral gap, inequality [23, 6].”