Approximation numbers of embeddings of Sobolev spaces
type: Item
instance of: scholarly article
title: Approximation numbers of embeddings of Sobolev spaces
zbMATH Open document ID: 0841.46022
DOI: 10.1007/PL00004515
author: Alexei A. Ilyin
author: D. E. Edmunds
published in: Mathematische Zeitschrift
publication date: 1996-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/174842
review text: Under appropriate hypotheses on the domain \(\Omega\) in \(\mathbb{R}^{2m}\), upper bounds for the approximation numbers of the compact embeddings of \(\mathring H^m(\Omega)\) in \(L_q(\Omega)\) \((q\geq 2)\) and in a suitable Orlicz space are obtained in terms of eigenvalues of \((- \Delta)^m\) with zero Dirichlet conditions. The case of Neumann boundary conditions is also discussed, as is the situation when these embeddings are not compact.
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 861943
zbMATH Keywords: approximation numbers
zbMATH Keywords: compact embeddings
zbMATH Keywords: Orlicz space
zbMATH Keywords: eigenvalues
zbMATH Keywords: Dirichlet conditions
zbMATH Keywords: Neumann boundary conditions
MaRDI profile type: Publication
OpenAlex ID: W4231205854
description: scientific article; zbMATH DE number 861943