Parabolic equations with measurable coefficients
type: Item
instance of: scholarly article
title: Parabolic equations with measurable coefficients
zbMATH Open document ID: 1124.35024
author: N. V. Krylov
author: Doyoon Kim
published in: Potential Analysis
publication date: 2007-06-07T00:00:00Z
review text: The authors investigate the unique solvability of second order parabolic equations in non-divergence form \[ u_t+a^{jk}(t,x)u_{x^jx^k} +b^j(t,x)u_{x^j} +c(t,x)u=f \] in Sobolev spaces \(W^{1,2}_p((0,R)\times {\mathbb R}^d)\) with \(p\geq 2.\) The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 5162166
zbMATH Keywords: vanishing mean oscillation
zbMATH Keywords: non-divergence form
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s11118-007-9042-8
OpenAlex ID: W2138642886
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DOI: 10.1007/S11118-007-9042-8
description: scientific article; zbMATH DE number 5162166