Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space [PDF]
Entropy, 2018 We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant.
Ichiro Shigekawa
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The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality [PDF]
The Scientific World Journal, 2014 An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang’s result to any norm from Euclidean norm, and the geometric analogue of this inequality is given.
Shuai Liu, Binwu He
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Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. [PDF]
, 2012 The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the ...
Blower, Gordon
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Logarithmic Sobolev inequalities and spectral concentration for the cubic Shrödinger equation [PDF]
, 2014 The nonlinear Schr\"odinger equation $\NLSE(p, \beta)$, $-iu_t=-u_{xx}+\beta \vert u\vert^{p-2} u=0$, arises from a Hamiltonian on infinite-dimensional phase space $\Lp^2(\mT)$. For $p\leq 6$, Bourgain (Comm. Math. Phys. 166 (1994), 1--26) has shown that
Doust, Ian +2 more
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Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space
, 2023 Brendle recently proved a sharp Sobolev inequality and logarithmic Sobolev inequality for submanifolds in Euclidean space. From the sharp Sobolev inequality, he achieved a breakthrough in the conjecture of isoperimetric inequality for minimal ...
Ho, Pak-tung
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From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality [PDF]
, 2008 International audienceWe develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly ...
Gentil, Ivan
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Transportation of measure, Young diagrams and random matrices. [PDF]
, 2004 The theory of transportation of mesure for general cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration of measure inequality.
Blower, Gordon
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Weighted Sobolev spaces on curves [PDF]
, 2002 45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non ...
Pestana, Domingo +3 more
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Compact embeddings of broken Sobolev spaces and applications [PDF]
, 2009 In this paper, we present several extensions of theoretical tools for the analysis of discontinuous Galerkin (DG) method beyond the linear case.
Buffa, Annalisa, Ortner, Christoph
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Advanced Nonlinear Studies, 2022 In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa +2 more
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