Our next MORE seminar meeting will take place on Monday (April 18, 2016) at 9:00 am in K6. Sebastian Schwarzacher will continue with his lecture on Existence and regularity for a class of rate-independent systems. Please see the details below.
This talk will be about a recent work on rate-independent systems of a joint work with F. Rindler. 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 talk, 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.