Quantitative approximation theorems for elliptic operators
type: Item
instance of: scholarly article
title: Quantitative approximation theorems for elliptic operators
zbMATH Open document ID: 0851.30022
published in: Journal of Approximation Theory
publication date: 1996-12-01T00:00:00Z
review text: Let \(L(D)\) be an elliptic linear partial differential operator with constant coefficients and only highest order terms. For compact sets \(K \subset \mathbb{R}^N\) whose complements are John domains the authors prove a quantitative Runge theorem: if a function \(f\) satisfies \(L(D) f = 0\) on a fixed neighborhood of \(K\), they estimate the supnorm distance from \(f\) to the polynomial solutions of degree at most \(n\). The proof utilizes a two-constants theorem for solutions to elliptic equations. The authors then deduce versions of Jackson and Bernstein theorems for elliptic operators.
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 35J99
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35E20
zbMATH DE Number: 885471
zbMATH Keywords: Jackson theorem
zbMATH Keywords: Runge theorem
zbMATH Keywords: Bernstein theorems
author: Thomas Bagby
author: Len Bos
author: Norm Levenberg
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: jath.1996.0029
OpenAlex ID: W2070328676
DOI: 10.1006/JATH.1996.0029
description: scientific article; zbMATH DE number 885471