Parabolic equations with BMO coefficients in Lipschitz domains
type: Item
instance of: scholarly article
title: Parabolic equations with BMO coefficients in Lipschitz domains
zbMATH Open document ID: 1061.35021
author: Sun-Sig Byun
published in: Journal of Differential Equations
publication date: 2005-02-22T00:00:00Z
review text: The present paper deals with certain Sobolev-type estimates for the weak solutions of the following initial-boundary value problem for a uniformly parabolic operator \[ \begin{cases} u_t-(a_{ij}u_{x_j})_{x_i}=u_t- \operatorname{div} (A\nabla u)= \operatorname{div} {\mathbf f} & \text{ in } \Omega_T,\\ u=0 & \text{ on } \partial_p\Omega_T. \end{cases} \] The geometric setting is that of time-independent cylinders having a space intersection assumed to be locally given by graphs with small Lipschitz coefficients, the parabolic constants of the operator. There are proved relevant \(L^p\) estimates, assuming that the coefficients are in the parabolic class of functions with bounded mean oscillation (BMO) with small enough BMO-seminorm.
reviewed by: Lubomira Softova
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 2136114
zbMATH Keywords: small BMO coefficients
zbMATH Keywords: maximal function
zbMATH Keywords: Vitali covering lemma
MaRDI profile type: Publication
full work available at URL: j.jde.2004.08.018
OpenAlex ID: W2022349341
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DOI: 10.1016/J.JDE.2004.08.018
description: scientific article; zbMATH DE number 2136114