Rellich and Calderón-Zygmund inequalities for an operator with discontinuous coefficients
type: Item
instance of: scholarly article
title: Rellich and Calderón-Zygmund inequalities for an operator with discontinuous coefficients
zbMATH Open document ID: 1372.47054
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2016-08-11T00:00:00Z
review text: The authors provide necessary and sufficient conditions for the validity of the Rellich and the Calderón-Zygmund inequalities in \(L^p(\mathbb{R}^N)\) for the operator \[ L=\Delta +(a-1)\sum_{i,j=1}^N \dfrac{x_ix_j}{|x|^2}D_{ij}+c\dfrac{x}{|x|^2}\cdot\nabla - \dfrac{b}{|x|^2} \] with \(a>0\) and \(b,c\in\mathbb{R}.\) The approach is that of the authors' paper [Math. Ann. 361, No. 1--2, 313--366 (2015; Zbl 1318.26038)] applied to the operator \[ \tilde L= |x|^\alpha\Delta +\tilde c |x|^{\alpha-1}\dfrac{x}{|x|}\cdot \nabla -\tilde b |x|^{\alpha-2} \] with suitable \(\alpha,\) \(\tilde{c}\) and \(\tilde{c}.\)
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6614277
zbMATH Keywords: elliptic operator
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: Rellich inequalities
zbMATH Keywords: Calderón-Zygmund inequalities
author: Giorgio Metafune
author: Motohiro Sobajima
author: Chiara Spina
reviewed by: Dian K. Palagachev
MaRDI profile type: Publication
full work available at URL: s10231-015-0517-8
OpenAlex ID: W1109515278
cites work: Rellich inequalities with weights
cites work: Q4041031
cites work: Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
cites work: Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
cites work: Linear and quasilinear elliptic equations
cites work: Su un operatore ellittico a coefficienti discontinui
cites work: Q4402371
cites work: Q5489594
cites work: Elliptic operators with unbounded diffusion coefficients in \(L^p\) spaces
cites work: Weighted Calderón-Zygmund and Rellich inequalities in \(L^p\)
cites work: A degenerate elliptic operator with unbounded diffusion coefficients
cites work: Elliptic operators with unbounded diffusion and drift coefficients in \(L^p\)
cites work: On a class of elliptic operators with unbounded diffusion coefficients
cites work: A simple approach to Hardy inequalities
cites work: Q3125854
cites work: Second order elliptic operators with diffusion coefficients growing as \(|x|^\alpha\) at infinity
cites work: Q5580541
DOI: 10.1007/S10231-015-0517-8
description: scientific article; zbMATH DE number 6614277