Regularity of weak solutions to rate-independent systems in one-dimension

TL;DR

This paper proves that weak solutions to certain one-dimensional rate-independent systems exhibit regularity properties such as being SBV, having finite jumps, or being piecewise $C^1$, based on assumptions on the energy functional.

Contribution

It establishes regularity results for weak solutions of rate-independent systems without requiring convexity of the energy functional.

Findings

Weak solutions are of class SBV or have finite jumps.

Solutions can be piecewise $C^1$ under certain conditions.

Regularity results hold without convexity assumptions.

Abstract

We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate-independent system is of class SBV, or has finite jumps, or is even piecewise $C^1$. Our assumption is essentially imposed on the energy functional, but not convexity is required.