# The maximal monotonicity of the subdifferential in locally convex spaces via upper envelopes

## TL;DR

This paper investigates conditions under which the convex subdifferential is maximally monotone in locally convex spaces, providing a general theoretical framework for understanding subdifferential properties.

## Contribution

It introduces equivalent conditions for maximal monotonicity of the subdifferential in the broad setting of locally convex spaces, extending existing theory.

## Key findings

- Characterization of maximal monotonicity conditions
- Extension of subdifferential theory to locally convex spaces
- Theoretical framework for upper envelope representations

## Abstract

Abstract Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.