On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients
type: Item
instance of: scholarly article
title: On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients
zbMATH Open document ID: 1473.35085
author: Hongjie Dong
author: Xinghong Pan
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-07-22T00:00:00Z
review text: The paper deals with weak solutions to conormal derivative problem for linear, uniformly parabolic operators of the form \[ \partial_t u -\sum_{i,j=1}^nD_i\big( a^{ij}(x,t)D_ju+a^i(x,t)u\big)+\sum_{i=1}^n b^i(x,t)D_iu+c(x,t)u. \] The coefficients \(a^{ij}\) and \(a\) are supposed to have Dini mean oscillation while \(b^i\) and \(c\) belong to \(L^q\) with \(q>n+2.\) Assuming suitable Dini regularity of the boundary, the authors prove continuous differentiablity of the weak solutions up to the boundary.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 7373630
zbMATH Keywords: Dini mean oscillation coefficients
zbMATH Keywords: conormal derivative problem
zbMATH Keywords: parabolic equations
MaRDI profile type: Publication
full work available at URL: dcds.2021049
OpenAlex ID: W3138264435
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DOI: 10.3934/DCDS.2021049
description: scientific article; zbMATH DE number 7373630