Abstract:
We consider variational problems with differential constraints, which emanate from materials science and the study of compensated compactness. While the lower-semicontinuity in this setting has been well understood, one prominent work being the equivalence of the lower semicontinuity and the quasi-convexity condition by Fonseca and Müller under the constant rank assumption, much less is known regarding regularity. I will first give a short introduction to this type of problems, and then talk about how to establish regularity, including higher integrability and partial continuity, despite the degeneracy inherent to the constant rank condition. This talk is based on joint work with Christopher Irving and Bogdan Raiță.
Biography:
Zhuolin Li is a Postdoctoral Researcher at the Max Planck Institute in Leipzig, working with László Székelyhidi. She received her BSc in Mathematics from Peking University in 2018 and her DPhil in Mathematics from the University of Oxford in 2023 under the supervision of Jan Kristensen. From August 2023 to March 2024, she was a Postdoctoral Fellow at SLMath (MSRI), where she worked with Tatiana Toro.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.