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; regularity for almost minimizers of anisotropic fractional perimeters; regularity for the isoperimetric problem with double density.