Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 475-484

HOPF'S LEMMA FOR A CLASS OF SINGULAR/DEGENERATE PDE-S

Hayk Mikayelyan and Henrik Shahgholian

Xi'an Jiaotong-Liverpool University, Department of Mathematical Sciences
Ren Ai Lu 111, 215123 Suzhou, Jiangsu Province, P.R. China; Hayk.Mikayelyan 'at' xjtlu.edu.cn

Royal Institute of Technology (KTH), Department of Mathematics
100 44 Stockholm, Sweden; henriksh 'at' math.kth.se

Abstract. This paper concerns Hopf's boundary point lemma, in certain C^1,Dini-type domains, for a class of singular/degenerate PDE-s, including p-Laplacian. Using geometric properties of levels sets for harmonic functions in convex rings, we construct sub-solutions to our equations that play the role of a barrier from below. By comparison principle we then conclude Hopf's lemma.

2010 Mathematics Subject Classification: Primary 35J25, 35J70.

Key words: Partial differential equations, regularity.

Reference to this article: H. Mikayelyan and H. Shahgholian: Hopf's lemma for a class of singular/degenerate PDE-s. Ann. Acad. Sci. Fenn. Math. 40 (2015), 475-484.

Full document as PDF file

doi:10.5186/aasfm.2015.4033