Entropy and approximation numbers of weighted Sobolev spaces via bracketing

Abstract

We investigate the asymptotic behaviour of entropy and approximation numbers of the compact embedding id :Here E m p,σ (B) denotes a Sobolev space with a power weight perturbed by a logarithmic function. The weight contains a singularity at the origin. Inspired by Evans and Harris [5], we apply a bracketing technique which is an analogue to that of Dirichlet-Neumann-bracketing used by Triebel in [14] for p = 2.

Kolmogorov Widths of Weighted Sobolev Classes on an Interval with Conditions on the Zeroth and First Derivatives

“…In this paper we obtain the estimates for the linear widths of a set M in the space L q,v (Ω). The problem on estimating the Kolmogorov and linear widths of weighted Sobolev classes with different constraints on the derivatives was studied in [2][3][4][5][6][7][8][9][10][11][12][13][14]. For details, see [1].…”