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Homepage of Bozhidar Velichkov

Professore Ordinario (Full Professor) at
Dipartimento di Matematica
Università di Pisa

I am working in the fields of
Calculus of Variations and Partial Differental Equations.
I am interested in the so-called Regularity Theory, which is the study of the fine structure of the solutions to variational and PDE problems.
Most of my current research is dedicated to Free Boundary Problems.

*NEW*


• Epsilon-regularity for the solutions of a free boundary system.
(with Francesco Paolo Maiale and Giorgio Tortone)


• Regularity of the optimal sets for the second Dirichlet eigenvalue
(with Dario Mazzoleni and Baptiste Trey) - Summary/Cover letter


• Regularity of the two-phase free boundaries - the extended version of the Oberwolfach report of my talk at the 2020 workshop Calculus of Variations.


• Regularity of the free boundary for the two-phase Bernoulli problem
(with Guido De Philippis and Luca Spolaor) - Summary/Cover letter


• Regularity of the two-phase free boundaries - slides of my talks in Pisa and Levico


• Regularity of the one-phase free boundaries - Lecture notes


• On the logarithmic epiperimetric inequality - slides of my talks in
Krakow, Aveiro, Oberwolfach, Trento, and Milano