Existence and regularity for a class of rate-independent systems

TL;DR

This paper proves the existence of H"older-regular strong solutions for a class of rate-independent systems, advancing the understanding of their regularity properties beyond weak solutions.

Contribution

It introduces a method to establish higher regularity of solutions for rate-independent systems using time-discrete approximation and elliptic regularity estimates.

Findings

Existence of H"older-regular strong solutions

Higher regularity results for solutions

Application of Rothe approximation and elliptic estimates

Abstract

Despite the many applications of rate-independent systems, their regularity theory is still largely unexplored. Usually, only weak solution with potentially very low regularity are considered, which requires non-smooth techniques. In this work, however, we directly prove the existence of H\"older-regular strong solutions for a class of rate-independent systems. We also establish further assertions about higher regularity of our solutions. The proof proceeds via a time-discrete Rothe approximation, careful elliptic regularity estimates in the discrete situation and evolutionary techniques.