The equality of mixed partial derivatives under weak differentiability conditions
History and Overview
2015-08-04 v3 Classical Analysis and ODEs
Abstract
We review and develop two little known results on the equality of mixed partial derivatives which can be considered the best results so far available in their respective domains. The former, due to Mikusi\'nski and his school, deals with equality at a given point, while the latter, due to Tolstov, concerns equality almost everywhere. Applications to differential geometry and General Relativity are commented.
Cite
@article{arxiv.1309.5841,
title = {The equality of mixed partial derivatives under weak differentiability conditions},
author = {E. Minguzzi},
journal= {arXiv preprint arXiv:1309.5841},
year = {2015}
}
Comments
17 pages. v2: Added reference to Mikusinski's works. v3: Corrected a product set statement in Theorem 6