Partial regularity for parabolic systems with VMO-coefficients
type: Item
instance of: scholarly article
title: Partial regularity for parabolic systems with VMO-coefficients
zbMATH Open document ID: 1472.35080
author: Leon Mons
published in: Communications on Pure and Applied Analysis
publication date: 2021-06-16T00:00:00Z
review text: The author studies the regularity properties of the solutions of the following parabolic system in divergence form \[ u_t-\mathrm{div} A(x,t,u,Du)=0 \qquad \text{ in } \Omega_T=\Omega\times(-T,0)) \] It is established a partial Hölder regularity result for the weak solutions imposing standard \(p\)-growth condition and ellipticity condition on the principal operator. The vector-function \(A\) is discontinuous in \((x,t)\) verifying a VMO-type condition. The parabolic structure of the operator requires the use of suitable intrinsic cylinders that permit to apply the method of \(\mathcal{A}\)-caloric approximation.
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 7359968
zbMATH Keywords: \(p\)-growth condition
zbMATH Keywords: partial regularity
zbMATH Keywords: intrinsic geometry
zbMATH Keywords: \(\mathcal{A}\)-caloric approximation
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: cpaa.2021041
OpenAlex ID: W3148845603
cites work: Regularity in parabolic Dini continuous systems
cites work: Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients
cites work: Regularity in parabolic systems with continuous coefficients
cites work: Equazioni paraboliche del secondo ordine e spazi \({\mathfrak L}^{2,\theta} (\Omega,\delta)\)
cites work: Differentiability of the solutions of nonlinear elliptic systems with natural growth
cites work: Partial regularity of minimizers of quasiconvex integrals with subquadratic growth
cites work: Spazi \({\mathcal L}^{(p,\vartheta)} (\Omega,\delta)\) e loro proprieta
cites work: Q5537959
cites work: Q3308449
cites work: Degenerate parabolic equations
cites work: Optimal interior partial regularity for nonlinear elliptic systems: The method of \(A\)-harmonic approximation
cites work: Second order parabolic systems, optimal regularity, and singular sets of solutions
cites work: Harmonic type approximation lemmas
cites work: Parabolic Systems with Polynomial Growth and Regularity
cites work: Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals
cites work: Partial regularity for subquadratic parabolic systems with continuous coefficients
cites work: Partial continuity for elliptic problems
cites work: Q3151387
cites work: Partial regularity results for minimizers of quasiconvex functionals of higher order
cites work: Q5562267
cites work: Regularity of minima: an invitation to the dark side of the calculus of variations.
cites work: Continuity of Solutions of Parabolic and Elliptic Equations
cites work: Partial regularity for subquadratic parabolic systems by \(\mathcal{A}\)-caloric approximation
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Q4856928
DOI: 10.3934/CPAA.2021041
description: scientific article; zbMATH DE number 7359968