Transversally Lipschitz harmonic functions are Lipschitz

Abstract

ABSTRACT. Let Ω ⊂ R n be a bounded domain with C ∞ boundary. We show that a harmonic function in Ω that is Lipschitz along a family of curves transversal to bΩ is 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.

Tangential Lipschitz gain for holomorphic functions on domains of finite type

“…I started working on this project as part of my Ph.D. thesis [14] under his guidance at The Ohio State University and the results reported here were obtained during my stay at the Institute for Advanced Study. I wish to thank the Institute for Advanced Study for their hospitality.…”