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191
SOBOLEV REGULARITY AND AN ENHANCED JENSEN INEQUALITY
, 2007
"... Abstract. We derive a new criterion for a realvalued function u to be in the Sobolev space W 1,2 (R n). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values con ..."
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Abstract. We derive a new criterion for a realvalued function u to be in the Sobolev space W 1,2 (R n). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values
Logarithmic Sobolev inequality and finite markov chains
, 1996
"... This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous ti ..."
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Cited by 179 (15 self)
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This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous
Sobolev regularity via the convergence rate of convolutions and Jensen’s inequality
"... Abstract. We derive a new criterion for a realvalued function u to be in the Sobolev space W 1,2 (Rn). This criterion consists of comparing the value of a functional ∫ f (u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values con ..."
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Cited by 2 (0 self)
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Abstract. We derive a new criterion for a realvalued function u to be in the Sobolev space W 1,2 (Rn). This criterion consists of comparing the value of a functional ∫ f (u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values
Regularization of Wavelets Approximations
, 1999
"... this paper, weintroduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach can apply readily to many other statistical contexts. Various new penalty functions are proposed. The hardthresholding and s ..."
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Cited by 119 (16 self)
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to possess thresholding properties. Oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions. The sampling properties of nonlinear regularized wavelet estimators are established, and are shown to be adaptively minimax. To eciently solve penalized least
Geometrictype Sobolev inequalities and applications to the regularity of minimizers
, 2011
"... The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey’s inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the inequalities. Then, as main application of our inequalities, we estab ..."
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Cited by 6 (2 self)
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The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey’s inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the inequalities. Then, as main application of our inequalities, we
Symmetry and Regularity of Extremals of an Integral Equation related to the HardySobolev Inequality
, 2010
"... Let α be a real number satisfying 0 < α < n, 0 ≤ t < α, α∗(t) = 2(n−t) n−α. We consider the integral equation u(x) = ..."
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Cited by 4 (0 self)
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Let α be a real number satisfying 0 < α < n, 0 ≤ t < α, α∗(t) = 2(n−t) n−α. We consider the integral equation u(x) =
Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant
 SIAM J. Control Optimz
"... Abstract. In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H1(Ω) ↪ → Lq(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov eigenv ..."
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Cited by 12 (10 self)
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Abstract. In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H1(Ω) ↪ → Lq(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov
Nonlinear diffusions, hypercontractivity and the optimal L^pEuclidean logarithmic Sobolev inequality
, 2002
"... The equation u t = # p (u ) for p > 1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal L Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focus on the existence and t ..."
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Cited by 11 (3 self)
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and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the L inequality. A large deviation result based on a HamiltonJacobi equation and also related to the L Euclidean logarithmic Sobolev inequality
Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the LévyFokkerPlanck equation
"... Abstract. In this paper we study some applications of the Lévy logarithmic Sobolev inequality to the study of the regularity of the solution of the fractal heat equation, i. e. the heat equation where the Laplacian is replaced with the fractional Laplacian. It is also used to the study of the asympt ..."
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Cited by 2 (2 self)
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Abstract. In this paper we study some applications of the Lévy logarithmic Sobolev inequality to the study of the regularity of the solution of the fractal heat equation, i. e. the heat equation where the Laplacian is replaced with the fractional Laplacian. It is also used to the study
Results 1  10
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191