My research focuses on variational problems, which concern the optimisation (mostly minimisation) of certain energy functionals and the analysis of the corresponding minimisers.
I work on problems in the calculus of variations (CoV), especially regularity theory. Much of my research focus on problems that exhibit various types of degeneracy. I am also interested in geometric measure theory (GMT), and many geometric variational problems are closely related to their non-parametric counterparts in CoV, sharing similar insights and ideas.
Recently, I have also found free boundary problems and some questions arising from continuum mechanics particularly appealing.
My updated research statement can be found here.
Publications and preprints
1. Christopher Irving, Zhuolin Li and Bogdan Raita. Partial regularity for A-quasiconvex variational problems of linear growth. In preparation.
2. Panu Lahti and Zhuolin Li. Non-local functionals, total variation, and Gamma-convergence with respect to area-strict convergence. arXiv: 2502.06613
3. Zhuolin Li and Bogdan Raita. Partial regularity and higher integrability for A-quasiconvex variational problems. arXiv: 2412.10363
4. Zhuolin Li. Partial regularity for ω-minimizers of quasiconvex functionals. Calc. Var. Partial Differential Equations. 61 (2022), no. 178. arXiv:2201.11044