Speaker: 李卓琳博士，Max Planck Institute for Mathematics in the Sciences
Inviter:
Title: Variational problems with differential constraints: regularity under the constant rank condition
Language: English
Time & Venue: 2024.12.17 15:00-16:00 S813
Abstract: Many problems in physics, especially in materials science, can be formulated as variational problems with linear differential constraints. Such problems were first studied in the prototypical setup, where the differential operator involved is curl, and then in that of general differential constraints. The lower semicontinuity of those problems has been well understood, one prominent work being the equivalence of the lower semicontinuity and the quasi-convexity condition by Fonseca and M\”{u}ller under the constant rank assumption, while very little is know regarding of regularity. I will first talk about problems of this type, and then introduce a recent work, in which partial regularity and higher integrability are established under the constant rank condition. This talk is based on joint work with Bogdan Raita.
