G. Buttazzo, B. Velichkov:
Some New Problems in Spectral Optimization
(Preprint) 2012
B. Velichkov:
Existence and regularity results for some shape optimization problems
(Phd Thesis) 2013
D. Bucur, G. Buttazzo, B. Velichkov:
Shape Optimization Problems with Internal Constraint
Ann. I. H. Poincare' Anal. Non Lineaire Vol. 30, N. 3, p. 467--495, 2013
G. Buttazzo, A. Gerolin, B. Ruffini, B. Velichkov:
Optimal Potentials for Schrödinger Operators
J. Éc. polytech. Math. 2013
G. Buttazzo, B. Velichkov:
Shape optimization problems on metric measure spaces
J. Funct. Anal. Vol. 264, N. 1, p. 1--33, 2013
B. Bogosel, B. Velichkov:
A multiphase shape optimization problem for eigenvalues: qualitative study and numerical results
SIAM Numer. Anal. 2013
G. Buttazzo, M. van den Berg, B. Velichkov:
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
(Preprint) 2014
B. Velichkov:
A note on the monotonicity formula of Caffarelli-Jerison-Kenig
Rend. Lincei Mat. Appl. Vol. 25, p. 165--189, 2014
G. Buttazzo, B. Velichkov:
The spectral drop problem
(Preprint) 2014
G. Buttazzo, B. Ruffini, B. Velichkov:
Shape Optimization Problems for Metric Graphs
ESAIM Control Optim. Calc. Var. Vol. 20, N. 01, p. 1--22, 2014
D. Bucur, G. Buttazzo, B. Velichkov:
Spectral optimization problems for potentials and measures
SIAM J. Math. Anal. 2014
G. De Philippis, B. Velichkov:
Existence and regularity of minimizers for some spectral functionals with perimeter constraint
Appl. Math. Optim. Vol. 69, N. 2, p. 199--231, 2014
D. Bucur, B. Velichkov:
Multiphase shape optimization problems
SIAM J. Control Optim. 2014
L. Brasco, G. De Philippis, B. Velichkov:
Faber-Krahn inequalities in sharp quantitative form
Duke Math. J. Vol. 164, N. 9, p. 1777-1832, 2015
G. De Philippis, A. R. Mészáros, F. Santambrogio, B. Velichkov:
BV Estimates in Optimal Transportation and Applications
Arch. Ration. Mech. An. (Accepted Paper) 2015
G. Buttazzo, E. Oudet, B. Velichkov:
A free boundary problem arising in PDE optimization
Calc. Var. PDE 2015
D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov:
Lipschitz regularity of the eigenfunctions on optimal domains
Arch. Rat. Mech. Anal. 2015
A. Massaccesi, E. Oudet, B. Velichkov:
Numerical Calibration of Steiner trees
Appl. Math. Optim. 2016
J. C. Bellido, G. Buttazzo, B. Velichkov:
Worst-case shape optimization for the Dirichlet energy
Nonlinear Analysis 2016
G. De Philippis, J. Lamboley, M. Pierre, B. Velichkov:
Regularity of Minimizers of Shape Optimization Problems involving Perimeter
J. Math. Pures Appl. 2016
L. Spolaor, B. Velichkov:
An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case
Comm. Pure Appl. Math. (Accepted Paper) p. 32, 2017
D. Mazzoleni, S. Terracini, B. Velichkov:
Regularity of the optimal sets for some spectral functionals
Geom. Funct. Anal. 2017
M. Colombo, L. Spolaor, B. Velichkov:
A logarithmic epiperimetric inequality for the obstacle problem
Geom. Funct. Anal. (Accepted Paper) 2017
D. Bucur, I. Fragalà, B. Velichkov, G. Verzini:
On the honeycomb conjecture for a class of minimal convex partitions
Trans. Amer. Math. Soc. (Accepted Paper) 2017
G. Buttazzo, B. Velichkov:
A shape optimal control problem and its probabilistic counterpart
SIAM J. Math. Anal. (Accepted Paper) p. 16, 2017
G. Buttazzo, B. Velichkov:
Spectral optimization problems for Schrödinger operators
(Book Chapter) 2017
M. Colombo, L. Spolaor, B. Velichkov:
Direct epiperimetric inequalities for the thin obstacle problem and applications
Comm. Pure Appl. Math. (Accepted Paper) 2017
G. Buttazzo, F. Maestre, B. Velichkov:
Optimal potentials for problems with changing sign data
Journal of Optimization Theory and Applications 2017
M. Engelstein, L. Spolaor, B. Velichkov:
(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents
Geom. Topol. (Accepted Paper) 2018
L. Spolaor, B. Trey, B. Velichkov:
Free boundary regularity for a multiphase shape optimization problem
Communications in Partial Differential Equations (Accepted Paper) 2018
M. Colombo, L. Spolaor, B. Velichkov:
On the asymptotic behavior of the solutions to parabolic variational inequalities
J. Reine Agnew. Math. (Accepted Paper) 2018
M. Engelstein, L. Spolaor, B. Velichkov:
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
Duke Math. J. (Accepted Paper) 2018
D. Mazzoleni, S. Terracini, B. Velichkov:
Regularity of the free boundary for the vectorial Bernoulli problem
Analysis & PDE (Accepted Paper) 2018
E. Russ, B. Trey, B. Velichkov:
Existence and regularity of optimal shapes for elliptic operators with drift
Calc. Var. PDE 2019
F. Générau, E. Oudet, B. Velichkov:
Numerical computation of the cut locus via a variational approximation of the distance function
(Preprint) 2020
S. Guarino Lo Bianco, D. A. La Manna, B. Velichkov:
A two-phase problem with Robin conditions on the free boundary
Journal de l'École polytechnique - Mathématiques 2020
M. Colombo, L. Spolaor, B. Velichkov:
Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem
Interfaces and Free Boundaries (Accepted Paper) 2021
G. Buttazzo, F. P. Maiale, B. Velichkov:
Shape optimization problems in control form
(Submitted Paper) 2021
G. De Philippis, M. Engelstein, L. Spolaor, B. Velichkov:
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
(Preprint) 2021
F. P. Maiale, G. Tortone, B. Velichkov:
The boundary Harnack principle on optimal domains
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (Accepted Paper) 2021
F. P. Maiale, G. Tortone, B. Velichkov:
Epsilon-regularity for the solutions of a free boundary system
Revista Matemática Iberoamericana (Accepted Paper) 2021
L. Spolaor, B. Velichkov:
On the logarithmic epiperimetric inequality for the obstacle problem
Mathematics in Engineering Vol. 3, p. 1--42, 2021
G. De Philippis, L. Spolaor, B. Velichkov:
Regularity of the free boundary for the two-phase Bernoulli problem
Inventiones mathematicae 2021
G. De Philippis, L. Spolaor, B. Velichkov:
(Quasi-)conformal methods in two-dimensional free boundary problems
J. Eur. Math. Soc. (Accepted Paper) 2021
S. Guarino Lo Bianco, D. A. La Manna, B. Velichkov:
Free boundary cluster with Robin condition on the transmission interface
(Submitted Paper) 2022
G. Buttazzo, F. P. Maiale, D. Mazzoleni, G. Tortone, B. Velichkov:
Regularity of the optimal sets for a class of integral shape functionals
(Preprint) 2022
N. Edelen, L. Spolaor, B. Velichkov:
A strong maximum principle for minimizers of the one-phase Bernoulli problem
Indiana Math. J. (Accepted Paper) 2022
F. Générau, E. Oudet, B. Velichkov:
Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality
Arch. Rat. Mech. Anal. (Accepted Paper) 2022
D. Mazzoleni, B. Trey, B. Velichkov:
Regularity of the optimal sets for the second Dirichlet eigenvalue
Ann. Inst. H. Poincaré Anal. Non Linéaire 2022
B. Velichkov:
Regularity of the one-phase free boundaries
Lecture Notes of the Unione Matematica Italiana, Springer (Lecture Notes) Vol. 28, 2023
N. Edelen, L. Spolaor, B. Velichkov:
The symmetric (log-)epiperimetric inequality and a decay-growth estimate
(Preprint) 2023
L. Ferreri, B. Velichkov:
A one-sided two phase Bernoulli free boundary problem
(preprint) 2023
L. Ferreri, B. Velichkov:
Regularity for one-phase Bernoulli problems with discontinuous weights
and applications
(preprint) 2023
D. Mazzoleni, G. Tortone, B. Velichkov:
On the dimension of the singular set in optimization problems with measure constraint
(Preprint) 2023
L. Ferreri, G. Tortone, B. Velichkov:
A capillarity one-phase Bernoulli free boundary problem
(preprint) 2023
L. Ferreri, L. Spolaor, B. Velichkov:
On the fine structure of the solutions to nonlinear thin two-membrane
problems in 2D
(preprint) 2024
R. Ognibene, B. Velichkov:
Boundary regularity of the free interface in spectral optimal partition
problems
(preprint) 2024