The APDE seminar on Monday, 3/18, will be given by Zhuolin Li (SLMath/MSRI) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: Degenerate variational problems under the constant rank condition

Abstract: Differential expressions involving non-elliptic operators emerge in various PDEs and variational principles that arise from materials science, fluids, differential geometry, etc. Despite their inherent degeneracy, such operators, under the constant rank condition, retain certain good properties of elliptic operators. In this talk, we will first give a short introduction to the study of vectorial problems in the calculus of variations, and then discuss quasi-convex variational problems involving constant rank operators. For clarity, exterior derivatives will be taken as a particular example for illustration. We will consider the existence, which can also be interpreted as a Sobolev-type regularity, as well as the corresponding partial regularity via an excess decay estimate strategy. This talk is based on an ongoing work with Bogdan Raiță.