Transversally Lipschitz Harmonic Functions are Lipschitz
Analysis of PDEs
2015-04-14 v1 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.1203.4641,
title = {Transversally Lipschitz Harmonic Functions are Lipschitz},
author = {Sivaguru Ravisankar},
journal= {arXiv preprint arXiv:1203.4641},
year = {2015}
}