Fisher information and continuity estimates for nonlinear but 1-homogeneous diffusive PDEs (via the JKO scheme)

TL;DR

This paper demonstrates that for a class of 1-homogeneous diffusive PDEs, Fisher information remains bounded or decreases over time, and solutions preserve their moduli of continuity, using the JKO scheme.

Contribution

It introduces a novel application of the JKO scheme to establish bounds on Fisher information and continuity preservation for these PDEs.

Findings

Fisher information is bounded or decreases over time.

Moduli of continuity are conserved in solutions.

The JKO scheme effectively analyzes these properties.

Abstract

In this short paper we prove, using the JKO scheme, that quantities such as the Fisher information stay bounded or decrease across time for a family of 1-homogeneous diffusive PDEs. As a corollary, we prove that moduli of continuity are conserved across time for the solutions of those PDEs.