The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

for any density function p(x) on R, where pi(·|y1, . . . , yi−1, yi+1, . . . , yn) and Qi(·|x1, . . . , xi−1, xi+1, . . . , xn) denote the local specifications of p resp. q, and ρi is the logarithmic Sobolev constant of Qi(·|x1, . . . , xi−1, xi+1, . . . , xn). Thereby we derive a logarithmic Sobolev inequality for a weighted Gibbs sampler governed by the local specifications of q. Moreover, th...

In this paper we present an overview on logarithmic Sobolev inequalities. These inequalities have become a subject of intense research activity during the past years, from analysis and geometry in finite and infinite dimension, to probability and statistical mechanics, and of course many others developments and applications are expected. We have divided this paper into three parts. The first pa...

Motivated by some recent work in active contour applications, we study the use of Sobolev gradients for PDE-based image diffusion and sharpening. We begin by studying, for the case of isotropic diffusion, the gradient descent/ascent equation obtained by modifying the usual metric on the space of images, which is the L metric, to a Sobolev metric. We present existence and uniqueness results for ...

Let be introduced the Sobolev-type inner product (f, g) = 1 2 Z 1 −1 f(x)g(x)dx + M [f ′(1)g′(1) + f ′(−1)g′(−1)], where M ≥ 0. In this paper we will prove that for 1 ≤ p ≤ 4 3 there are functions f ∈ L([−1, 1]) whose Fourier expansion in terms of the orthonormal polynomials with respect to the above Sobolev inner product are divergent almost everywhere on [−1, 1]. We also show that, for some v...

As a follow-up of Haberl-Schuster’s “Asymmetric affine Lp Sobolev inequalities” and Cianchi-Lutwak-Yang-Zhang’s “Affine Moser-Trudinger and Morrey-Sobolev inequalities”, we establish sharp Moser-Trudinger and MorrySobolev inequalities induced by the positive part of a directional derivative on the unit Euclidean sphere. 1. Theorem In their 2009 JFA paper [1], Haberl-Schuster prove the following...

The equation ut = ∆p(u 1/(p−1)) 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 Lp-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focuse on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hype...

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

– Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of Hamilton–Jacobi equations. By the infimum-convolution description of the Hamilton–Jacobi solutions, this approach provides a clear view of the connection between logarithmic Sobo...