Homological differential calculus
Algebraic Topology
2019-06-20 v2 Optimization and Control
Symplectic Geometry
Abstract
This article provides a definition of a subdifferential for continuous functions based on homological considerations. We show that it satisfies all the requirement for a good notion of subdifferential. Moreover, we prove sublinearity, a Leibniz formula and an approximation result. This work fits in the framework of microlocal analysis of sheaves for C^0 symplectic problems and application to Aubry-Mather theory.
Cite
@article{arxiv.1310.4845,
title = {Homological differential calculus},
author = {Nicolas Vichery},
journal= {arXiv preprint arXiv:1310.4845},
year = {2019}
}