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arXiv · 1602.08701

Existence and regularity for a class of rate-independent systems

Filip Rindler·Sebastian Schwarzacher
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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.

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Filip Rindler, Sebastian Schwarzacher. 2016-02-28. Existence and regularity for a class of rate-independent systems. https://arxiv.org/abs/1602.08701

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