Nondivergence elliptic equations with unbounded coefficients
type: Item
instance of: scholarly article
title: Nondivergence elliptic equations with unbounded coefficients
zbMATH Open document ID: 1178.35149
author: Luigi Greco
author: Gioconda Moscariello
author: Teresa Radice
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2009-02-19T00:00:00Z
review text: The authors study the Dirichlet problem associated to the second order elliptic equation in nondivergence form \[ L=\sum_{i,j=1}^{n} a_{ij} (x) u_{x_i x_j}=f \] in a domain \(\mathbb R^n, \) \(n \geq 2\), \(f\) in \(L^2(\mathbb R^n) \) and, as in the main theorem, in \(L^2\log^\alpha(\mathbb R^n)\). The coefficients \(a_{ij} \) are assumed to be in the John-Nirenberg class of bounded mean oscillation functions and satisfy the ellipticity condition, not uniformly. The authors also discuss the case that \(a_{ij}\) are in the Sarason class of vanishing mean oscillation functions. We stress that the regularity result obtained do not rely on the representation formula of the derivatives of the solutions but they prove the estimate from below, considering that the second order minors of the Hessian matrix lie in the Hardy space \(H^1,\) and the well known \(H^1\)-BMO duality.
reviewed by: Maria Alessandra Ragusa
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5509385
zbMATH Keywords: elliptic equations
zbMATH Keywords: unbounded coefficients
zbMATH Keywords: bounded mean oscillation functions
zbMATH Keywords: Zygmund class
MaRDI profile type: Publication
full work available at URL: dcdsb.2009.11.131
OpenAlex ID: W1996493198
DOI: 10.3934/DCDSB.2009.11.131
description: scientific article; zbMATH DE number 5509385