The \(W^{1,2}_{( p,q )}\)-solvability for a class of fully nonlinear parabolic equations
type: Item
instance of: scholarly article
title: The \(W^{1,2}_{( p,q )}\)-solvability for a class of fully nonlinear parabolic equations
zbMATH Open document ID: 1475.35091
author: Hong Tian
author: Shenzhou Zheng
published in: Journal of Elliptic and Parabolic Equations
publication date: 2021-08-09T00:00:00Z
review text: The authors consider the following Cauchy-Dirichlet problem for fully nonlinear parabolic equations \[ \begin{cases} u_t*H(D^2u, Du, u, x, t)=0 & \text{ in } \Omega_T,\\ u=0 & \text{ on } \partial \Omega_T, \end{cases} \] where \(\Omega_T\) is a parabolic cylinder, \(\Omega\subset\mathbb{R}^d\), and \(\partial\Omega\in C^{1,1}\). The nonlinear term is supposed to be in BMO with respect to \((x,t)\). It is proved solvability in the Sobolev-Lorentz spaces \( W^{1,2}_{(p,q)}(\Omega_T) \) with \(p>d+1\), \(q>0\). The approach make use of the Fefferman-Stein inequality in the Lorentz spaces.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 7379839
zbMATH Keywords: fully nonlinear parabolic equations
zbMATH Keywords: BMO nonlinearities
zbMATH Keywords: Fefferman-Stein theorem
zbMATH Keywords: sharp functions
zbMATH Keywords: Lorentz spaces
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s41808-020-00094-6
OpenAlex ID: W3120701348
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DOI: 10.1007/S41808-020-00094-6
description: scientific article; zbMATH DE number 7379839