Coercive estimates for linear differential operators with constant coefficients
type: Item
instance of: scholarly article
title: Coercive estimates for linear differential operators with constant coefficients
zbMATH Open document ID: 1028.35041
DOI: 10.1023/A:1010271212457
author: N. N. Romanovskiĭ
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Let \(Q\) be a linear homogeneous differential operator of order \(k\) with constant coefficients and finite-dimensional kernel. The goal of this note is to construct a family of linear projection operators \(P_Q\) that satisfies \[ \begin{cases} \|P_Q u\|_{W^k_p(\Omega)}= C(\Omega,Q)\|u\|_{L^1(\Omega)},\\ \|u- P_Qu\|_{W^k_p(\Omega)}\leq C(\Omega, Q)\|Qu\|_{L_p(\Omega)}\end{cases},\tag{1} \] where \(\Omega\) is a given open set in \(\mathbb{R}^n\). To this end, the author uses the Sobolev integral representation only, which provides to obtain (1) for any homogeneous differential operator with constant coefficients provided that the kernel of the operator is finite-dimensional.
Mathematics Subject Classification ID: 35E20
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 1927764
zbMATH Keywords: projection operators
zbMATH Keywords: Sobolev integral representation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1927764