Transversally Lipschitz Harmonic Functions are Lipschitz

Details Transversally Lipschitz Harmonic Functions are Lipschitz Transversally Lipschitz Harmonic Functions are Lipschitz

2012-03-21

arxiv.org/abs/1203.4641v1

Mathematics

Analysis of PDEs

Scientific paper

Let \Omega\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We
show that a harmonic function in \Omega that is Lipschitz along a family of
curves transversal to b\Omega is Lipschitz in \Omega. The space of Lipschitz
functions we consider is defined using the notion of a majorant which is a
certain generalization of the power functions t^\alpha, 0<\alpha<1.

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