A Note on Flux Integrals over Smooth Regular Domains
Differential Geometry
2016-01-20 v2
Abstract
We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to numerical computation of a flux through the boundary of a domain, for example, when there is a large variation in the normal vector near a point. We present applications of this result to occupational measures and two-dimensional differential equations, including a new proof that all minimal invariant sets in the plane are trivial.
Cite
@article{arxiv.1310.3874,
title = {A Note on Flux Integrals over Smooth Regular Domains},
author = {Ido Bright and John M. Lee},
journal= {arXiv preprint arXiv:1310.3874},
year = {2016}
}