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# Analysis

### International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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ISSN
2196-6753
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Volume 35, Issue 1

# Partial boundary regularity of non-linear parabolic systems in low dimensions

Verena Bögelein
Published Online: 2014-12-15 | DOI: https://doi.org/10.1515/anly-2014-1287

## Abstract

In this paper we establish partial boundary regularity for non-linear parabolic systems ${\partial }_{t}u-diva\left(x,t,u,Du\right)=0$ with quadratic growth in dimensions $n\le 2$. In particular, we prove that almost every lateral boundary point is a Hölder continuity point for the spatial gradient of the solution. We are also able to treat particular vector fields in the higher dimensional case. In the case of vector fields $a\left(x,t,Du\right)$ not depending on u, the partial boundary regularity has been established in [Ann. Inst. H. Poincaré, Anal. Non Linéaire 27 (2010), 145–200].

MSC: 35D10; 35K55

Revised: 2014-11-26

Accepted: 2014-11-27

Published Online: 2014-12-15

Published in Print: 2015-03-01

Citation Information: Analysis, Volume 35, Issue 1, Pages 1–28, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747,

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