\(C^ m\) approximation by solutions of elliptic equations, and Calderón-Zygmund operators
type: Item
instance of: scholarly article
title: \(C^ m\) approximation by solutions of elliptic equations, and Calderón-Zygmund operators
zbMATH Open document ID: 0654.35007
DOI: 10.1215/S0012-7094-87-05509-8
author: J. Verdera
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Etant donnés un compact K de \({\mathbb{R}}^ n\), L un opérateur différentiel elliptique à coefficients constants de degré r et f une fonction de \(C^ m(v)\) (où v est un voisinage ouvert de K et m un entier \(\geq r)\) solution de (*) \(Lf=0\) l'auteur montre qu'il est possible d'``approcher'' (au sens de \(C^ m)\) f dans un voisinage de K par des fonctions de \(C^ m({\mathbb{R}}^ n)\), solutions de (*). Elle donne, en outre, une caractérisation géométrique d'un résultat d'approximation analogue.
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 4067410
zbMATH Keywords: approximation
zbMATH Keywords: Hausdorff content
zbMATH Keywords: Fourier analysis
zbMATH Keywords: geometric characterization
zbMATH Keywords: constant coefficients
reviewed by: Jean-Clarence Nosmas
MaRDI profile type: Publication
cites work: Approximation in the Mean by Solutions of Elliptic Equations
cites work: Q5583306
cites work: A Notion of Capacity Which Characterizes Removable Singularities
cites work: Removable singularities of solutions of linear partial differential equations
cites work: Q3671563
cites work: Q3933230
cites work: A constructive method for \(L^p\)-approximation by analytic functions
cites work: An Extremal Problem on Singular Integrals
cites work: Hausdorff Content and Rational Approximation in Fractional Lipschitz Norms
cites work: Q4149977
cites work: Q4087770
cites work: Q5607484
cites work: Approximation by rational modules in Sobolev and Lipschitz norms
cites work: On C m Rational Approximation
cites work: BMO Rational Approximation and One-Dimensional Hausdorff Content
cites work: The analytic capacity of sets in problems of approximation theory
full work available at URL: s0012-7094-87-05509-8
OpenAlex ID: W2028757398
description: scientific article; zbMATH DE number 4067410