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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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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


In this paper we establish partial boundary regularity for non-linear parabolic systems tu-diva(x,t,u,Du)=0 with quadratic growth in dimensions n2. 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(x,t,Du) not depending on u, the partial boundary regularity has been established in [Ann. Inst. H. Poincaré, Anal. Non Linéaire 27 (2010), 145–200].

Keywords: Boundary regularity; partial regularity; non-linear parabolic systems; singular set

MSC: 35D10; 35K55

About the article

Received: 2014-10-09

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, DOI: https://doi.org/10.1515/anly-2014-1287.

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