On the Morse-Sard Property and Level Sets of Sobolev and BV Functions
Analysis of PDEs
2015-12-15 v1 Classical Analysis and ODEs
Abstract
We establish Luzin and Morse-Sard properties for -functions defined on open domains in the plane. Using these results we prove that almost all level sets are finite disjoint unions of Lipschitz arcs whose tangent vectors are of bounded variation. In the case of -functions we strengthen the conclusion and show that almost all level sets are finite disjoint unions of -arcs whose tangent vectors are absolutely continuous.
Keywords
Cite
@article{arxiv.1007.4408,
title = {On the Morse-Sard Property and Level Sets of Sobolev and BV Functions},
author = {Jean Bourgain and Mikhail V. Korobkov and Jan Kristensen},
journal= {arXiv preprint arXiv:1007.4408},
year = {2015}
}