Bohdan Bulanyi

Research interests

Calculus of variations, partial differential equations, geometric measure theory.

Keywords: Regularity theory;  p-Laplace operator; free boundary; shape optimization; inverse problems; mean curvature flows; isoperimetric problems; Wulff shape; Riemannian manifold;  Sobolev mappings between manifolds; p-harmonic mappings; varifolds; homotopic Plateau problem;  minimal connections; Fokker-Planck equations; Hamilton-Jacobi equations; viscosity solution; weak optimal transport. 

Publications and preprints 

1. PDF Regularity for the planar optimal p-compliance problem, joint with A. Lemenant, ESAIM Control Optim. Calc. Var, 27:35, 2021. doi.org/10.1051/cocv/2021035 

2. PDF On the importance of the connectedness assumption in the statement of the optimal p-compliance problem, J. Math. Anal. Appl., 499:125064, 2021. doi.org/10.1016/j.jmaa.2021.125064 

3. PDF Partial regularity for the optimal p-compliance problem with length penalization, Calc. Var. Partial Differential Equations, 61:11, 2022. doi.org/10.1007/s00526-021-02073-8 

4. PDF Singular extension of critical Sobolev mappings under an exponential weak-type estimate, joint with J. Van Schaftingen, J. Funct. Anal., 288:110681, 2025. doi.org/10.1016/j.jfa.2024.110681 

5. PDF On the equivalence of static and dynamic weak optimal transport, To appear in Comptes Rendus Mathématique. doi.org/10.48550/arXiv.2311.13872 

6. PDF Limiting behavior of minimizing p-harmonic maps in 3d as p goes to 2 with finite fundamental group, joint with J. Van Schaftingen and B. Van Vaerenbergh, Arch. Ration. Mech. Anal., 249(3), 1-103, 2025. doi.org/10.1007/s00205-025-02086-z 

7. PDF Threshold dynamics approximation schemes for anisotropic mean curvature flows with a forcing term, joint with B. Ruffini, Nonlinear Anal., 261:113899, 2025. doi.org/10.1016/j.na.2025.113899  

8. PDF Regularity for optimal compliance problems with length penalization. PhD manuscript, 2021. 

Teaching

During my doctoral thesis, I was a teaching assistant (Allocataire - Moniteur) at the Université Paris 7 and then at the Université Paris Cité. The main practical classes taught were differential equations, numerical analysis, mathematical analysis and linear algebra. 

I am currently teaching the course Advanced topics in Mathematics 3 to students at the Master's level in Mathematics at the Université catholique de Louvain. This course examines in detail several problems related to Sobolev mappings between manifolds. 

Useful links

• ResearchGate 

• Google Scholar page 

• CVGMT page 

• ORCID