Allard-type boundary regularity for $C^{1,\alpha}$ boundaries
Analysis of PDEs
2014-09-11 v2
Abstract
In this paper we show boundary monotonicity formulae for rectifiable varifolds having a "boundary". In particular, we show that the area ratios of balls centered at this "boundary'' satisfy a nice monotonicity formula, similar to that for interior balls (proved in Allard's paper "On the first variation of a varifold''). This extends the boundary monotonicity formulae of Allard (see "On the first variation of a varifold- boundary behavior''), which require that the boundary is . As a corollary, Allard's boundary regularity results extend to this case and provide a regularity result for rectifiable varifolds with a ``boundary''.
Keywords
Cite
@article{arxiv.1008.4728,
title = {Allard-type boundary regularity for $C^{1,\alpha}$ boundaries},
author = {Theodora Bourni},
journal= {arXiv preprint arXiv:1008.4728},
year = {2014}
}