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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
.
Ufficio 42
Dipartimento di Matematica
Università di Pisa
bozhidar.velichkov@unipi.it
My page at CVGMT.
Selected
results
The one-phase Bernoulli problem
•
A capillarity one-phase Bernoulli free boundary problem
(with Lorenzo Ferreri, Giorgio Tortone)
•
Regularity for one-phase Bernoulli problems with discontinuous weights and applications
(with Lorenzo Ferreri)
•
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
(with Max Engelstein, Luca Spolaor)
Two-phase Bernoulli problems
•
A one-sided two phase Bernoulli free boundary problem
(with Lorenzo Ferreri)
•
(Quasi-)conformal methods in two-dimensional free boundary problems
(with Guido De Philippis, Luca Spolaor)
•
Regularity of the optimal sets for the second Dirichlet eigenvalue
(with Dario Mazzoleni, Baptiste Trey) -
Summary/Cover letter
•
Regularity of the free boundary for the two-phase Bernoulli problem
(with Guido De Philippis, Luca Spolaor)
-
Summary/Cover letter
-
Extended abstract - Workshop Calculus of Variations (Oberwolfach)
-
Slides of my talks in Pisa and Levico
•
An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case
(with Luca Spolaor,
Comm. Pure Appl. Math. 2018
)
Free boundary systems
•
On the dimension of the singular set in optimization problems with measure constraint
(with Dario Mazzoleni, Giorgio Tortone)
•
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
•
Direct epiperimetric inequalities for the thin obstacle problem and applications
(with Maria Colombo and
Luca Spolaor
,
Comm. Pure Appl. Math. 2019
)
•
A logarithmic epiperimetric inequality for the obstacle problem
(with Maria Colombo and
Luca Spolaor
,
GAFA - Geom. Funct. Anal. 2018
)
•
On the logarithmic epiperimetric inequality
- slides of my
talks in
Krakow, Aveiro, Oberwolfach, Trento, and Milano