Bohdan Bulanyi

I defended my PhD thesis on September 24, 2021 at the Université Paris Cité (formerly Université Paris Diderot) under the direction of Antoine Lemenant. In my dissertation I investigated the regularity and topological structure of a set minimizing the p-compliance functional with a length penalization. The key feature of my work was that I studied the regularity of minimizers for some free boundary type problem with a high codimensional free boundary set.

Then, until summer 2024, I was a postdoctoral researcher at the Université catholique de Louvain under the direction of Jean Van Schaftingen. I studied how the topology of a Riemannian manifold affects minimizers of p-energy functionals defined on Sobolev spaces of manifold-valued functions. I looked for extensions of Sobolev maps satisfying an exponential weak-type Sobolev estimate.

I am currently working with Berardo Ruffini and Eleonora Cinti at the University of Bologna. I work on anisotropic variational problems: BMO-type schemes for anisotropic mean curvature flows; regularity for almost minimizers of anisotropic fractional perimeters;

regularity for the isoperimetric problem with double density.

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E-mail: bohdan.bulanyi [at] unibo.it

Adress: Dipartimento di Matematica, Piazza di Porta San Donato 5, Bologna

Research interests

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

Keywords: regularity theory; elliptic PDEs; p-Laplace operator; free boundary; Sobolev maps; shape optimization; inverse problems; anisotropic mean curvature flow; anisotropic fractional perimeters; isoperimetric problem with double density; Wulff shape; weak optimal transport.

Publications and preprints

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
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
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
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
PDF On the equivalence of static and dynamic weak optimal transport, submitted. doi.org/10.48550/arXiv.2311.13872
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
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
PDF Regularity for optimal compliance problems with length penalization. PhD manuscript, 2021.

Teaching

2018--2019 (fall). Differential equations (teaching assistant), L2 Biology, Université Paris Diderot.
2018--2019 (spring). Numerical analysis (teaching assistant), L2 Mathematics, Université Paris Diderot.
2018--2019 (spring). Colloquia on calculus and linear algebra, L1 and L2 Mathematics, Université Paris Diderot.
2018--2019 (spring). Colloquia on calculus and linear algebra, L1 and L2 Mathematics, Université Paris Diderot.
2019--2020 (fall). Numerical analysis (teaching assistant), L2 Mathematics, Université Paris Diderot.
2019--2020 (spring). Colloquia on calculus and linear algebra, L1 and L2 Mathematics, Université Paris Diderot.
2020--2021 (fall). Calculus and linear algebra, L1 Chemistry, Université de Paris.
2020--2021 (spring). Tutoring in analysis and linear algebra, L1 Mathematics, Université de Paris.

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