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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.


The one-phase Bernoulli problem

Two-phase Bernoulli problems

Free boundary systems

Regularity of the optimal sets for a class of integral shape functionals
(with Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni, Giorgio Tortone)

The boundary Harnack principle on optimal domains
(with Francesco Paolo Maiale, Giorgio Tortone)

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

Regularity of the free boundary for the vectorial Bernoulli problem
(with Dario Mazzoleni, Susanna Terracini)

Regularity of the optimal sets for some spectral functionals

(with Dario Mazzoleni, Susanna Terracini)

Obstacle problems