Homological differential calculus

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.

References in corpus (1)

• Microlocal condition for non-displaceablility

Cited by in corpus (4)

• The Gromov-Eliashberg theorem by microlocal sheaf theory
• Spectral invariants towards a Non-convex Aubry-Mather theory
• On the supports in the Humilière completion and $\gamma$-coisotropic sets
• A microlocal characterization of Lipschitz continuity