Maximal regularity for elliptic operators with second-order discontinuous coefficients
type: Item
instance of: scholarly article
title: Maximal regularity for elliptic operators with second-order discontinuous coefficients
author: Luigi Negro
author: Giorgio Metafune
author: Chiara Spina
published in: Journal of Evolution Equations
publication date: 2022-01-03T00:00:00Z
review text: The authors consider the maximal regularity for parabolic problems associated to the second-order elliptic operator \[ L=\Delta +(a-1)\sum_{i,j=1}^N \frac{x_ix_j}{|x|^2}D_{ij}+\frac{c}{|x|^2}.\nabla -b |x|^{-1} \] with \(a>0\) and \(b,c\in \mathbb R.\) It is proved that the assocated parabolic problem \[ u_t(t)-Lu(t)=f(t)\quad t>0,\qquad u(0)=0 \] has maximal \(L^q\) regularity, that is for each \(f\in L^q(0,\infty;X)\) there exists a solution \(u\in W^{1,q}(0,\infty; X) \cap L^q(0,\infty; D(L)) \) where \(D(L)\) is the domain of \(L\) in \(X\).
Mathematics Subject Classification ID: 47F10
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 7451417
zbMATH Keywords: elliptic operators
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: kernel estimates
zbMATH Keywords: maximal regularity
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s00028-020-00637-3
OpenAlex ID: W3094042989
cites work: Weighted norm inequalities, off-diagonal estimates and elliptic operators. I: General operator theory and weights
cites work: Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse-square potentials and applications
cites work: Optimal kernel estimates for elliptic operators with second order discontinuous coefficients
cites work: ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
cites work: Analysis in Banach Spaces
cites work: Change of Variable Results for A p -and Reverse Holder RH r -Classes
cites work: Q4657003
cites work: Rellich inequalities in bounded domains
cites work: Sharp kernel estimates for elliptic operators with second-order discontinuous coefficients
cites work: Gradient estimates for elliptic operators with second-order discontinuous coefficients
cites work: Scale invariant elliptic operators with singular coefficients
cites work: Rellich and Calderón-Zygmund inequalities for an operator with discontinuous coefficients
cites work: Elliptic and parabolic problems for a class of operators with discontinuous coefficients
cites work: Kernel estimates for elliptic operators with second-order discontinuous coefficients
cites work: Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
cites work: Weighted Hardy spaces
DOI: 10.1007/S00028-020-00637-3
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description: scientific article; zbMATH DE number 7451417