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

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Published/Copyright: December 15, 2014

Abstract

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].

MSC: 35D10; 35K55
Received: 2014-10-9
Revised: 2014-11-26
Accepted: 2014-11-27
Published Online: 2014-12-15
Published in Print: 2015-3-1

© 2015 by De Gruyter

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