Topology of singular set of semiconcave function via Arnaud's theorem
Analysis of PDEs
2022-10-28 v1
Abstract
We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The proof is based on a theorem by Marie-Claude Arnaud (M.-C. Arnaud, \textit{Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation}. Nonlinearity, \textbf{24}(1): 71-78, 2011.). We also gave a new proof of the theorem in time-dependent case.
Keywords
Cite
@article{arxiv.2210.15646,
title = {Topology of singular set of semiconcave function via Arnaud's theorem},
author = {Tianqi Shi and Wei Cheng and Jiahui Hong},
journal= {arXiv preprint arXiv:2210.15646},
year = {2022}
}