Transversally Lipschitz Harmonic Functions are Lipschitz

Abstract

Let Ω\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We show that a harmonic function in Ωthat is Lipschitz along a family of curves transversal to bΩis Lipschitz in Ω. 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^α, 0<α<1.

Cited by in corpus (1)

• Tangential Lipschitz Gain for Holomorphic Functions on Domains of Finite Type