Gradient estimates of parabolic Cauchy-Dirichlet problems on Morrey-Banach spaces
type: Item
instance of: scholarly article
title: Gradient estimates of parabolic Cauchy-Dirichlet problems on Morrey-Banach spaces
zbMATH Open document ID: 1502.35033
author: Kwok-Pun Ho
published in: Journal of Elliptic and Parabolic Equations
publication date: 2022-11-02T00:00:00Z
review text: The paper provides gradient estimates in Morrey type spaces for the solutions of the Cauchy-Dirichlet problem for divergence form linear parabolic equations with discontinuous coefficients. Precisely, weak solutions of the equation \[ u_t(x,t)-\sum_{\alpha,\beta=1}^n D_\alpha\big(a^{\alpha\beta}(x,t)D_\beta u(x,t)\big)=\sum_{\alpha=1}^n D_\alpha f^\alpha(x,t),\quad (x,t)\in\Omega_T \] are considered with zero data on the parabolic boundary of the cylinder \(\Omega_T=\Omega\times (0,T).\) Assuming that the boundary of \(\Omega\) is Reifenberg flat and the principal coefficients \(a^{\alpha\beta}\) are measurable with respect to one spatial variable and of small bounded mean oscillation in the remaining space and time variables, the author derives gradient estimates for the weak solutions in Lorentz-Morrey, Orlicz-Morrey and Morrey spaces with variable exponents.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 7610713
zbMATH Keywords: Morrey spaces
zbMATH Keywords: Lorentz spaces
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: variable Lebesgue spaces
zbMATH Keywords: extrapolation theory
MaRDI profile type: Publication
full work available at URL: s41808-022-00174-9
OpenAlex ID: W4284961474
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DOI: 10.1007/S41808-022-00174-9
description: scientific article; zbMATH DE number 7610713