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.
Publications and preprints
1. Christopher Irving, Zhuolin Li and Bogdan Raita. Partial regularity for A-quasiconvex variational problems of linear growth. arXiv:2604.07538
2. Panu Lahti and Zhuolin Li. Non-local functionals, total variation, and Gamma-convergence with respect to area-strict convergence. SIAM Journal on Mathematical Analysis, 58 (2026), no. 3. 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 \omega-minimizers of quasiconvex functionals. Calc. Var. Partial Diļ¬erential Equations, 61 (2022), no. 178. arXiv:2201.11044