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
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. 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
G. Buttazzo, M. van den Berg, B. Velichkov:
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
Chapter in the book "New Trends in Shape Optimization" (Proceedings) 2015
G. De Philippis, A. R. Mészáros, F. Santambrogio, B. Velichkov:
BV Estimates in Optimal Transportation and Applications
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
D. Mazzoleni, S. Terracini, B. Velichkov:
Regularity of the optimal sets for some spectral functionals
Geom. Funct. Anal. 2017
G. Buttazzo, B. Velichkov:
Spectral optimization problems for Schrödinger operators
(Book Chapter) 2017
G. Buttazzo, F. Maestre, B. Velichkov:
Optimal potentials for problems with changing sign data
Journal of Optimization Theory and Applications 2017
L. Spolaor, B. Trey, B. Velichkov:
Free boundary regularity for a multiphase shape optimization problem
Communications in Partial Differential Equations 2018
G. Buttazzo, B. Velichkov:
A Shape Optimal Control Problem with Changing Sign Data
SIAM J. Math. Anal. 2018
M. Colombo, L. Spolaor, B. Velichkov:
A logarithmic epiperimetric inequality for the obstacle problem
Geom. Funct. Anal. 2018
D. Bucur, I. Fragalà, B. Velichkov, G. Verzini:
On the honeycomb conjecture for a class of minimal convex partitions
Trans. Amer. Math. Soc. 2018
E. Russ, B. Trey, B. Velichkov:
Existence and regularity of optimal shapes for elliptic operators with drift
Calc. Var. PDE 2019
L. Spolaor, B. Velichkov:
An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case
Comm. Pure Appl. Math. p. 32, 2019
M. Engelstein, L. Spolaor, B. Velichkov:
(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents
Geom. Topol. 2019
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
B. Velichkov:
Regularity of the one-phase free boundaries
Lecture Notes of the Unione Matematica Italiana, Springer (Lecture Notes) Vol. 28, 2020
M. Colombo, L. Spolaor, B. Velichkov:
Direct epiperimetric inequalities for the thin obstacle problem and applications
Comm. Pure Appl. Math. 2020
M. Engelstein, L. Spolaor, B. Velichkov:
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
Duke Math. J. 2020
M. Colombo, L. Spolaor, B. Velichkov:
On the asymptotic behavior of the solutions to parabolic variational inequalities
J. Reine Angew. Math. 2020
D. Mazzoleni, S. Terracini, B. Velichkov:
Regularity of the free boundary for the vectorial Bernoulli problem
Analysis & PDE 2020
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
G. De Philippis, L. Spolaor, B. Velichkov:
Regularity of the free boundary for the two-phase Bernoulli problem
Inventiones mathematicae 2021
L. Spolaor, B. Velichkov:
On the logarithmic epiperimetric inequality for the obstacle problem
Mathematics in Engineering Vol. 3, p. 1--42, 2021
M. Colombo, L. Spolaor, B. Velichkov:
Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem
Interfaces and Free Boundaries 2021
G. Buttazzo, F. P. Maiale, B. Velichkov:
Shape optimization problems in control form
Rend. Lincei Mat. Appl. 2021
S. Guarino Lo Bianco, D. A. La Manna, B. Velichkov:
Free boundary cluster with Robin condition on the transmission interface
(Submitted 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
F. Générau, E. Oudet, B. Velichkov:
Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality
Arch. Rat. Mech. Anal. 2022
G. Buttazzo, F. P. Maiale, D. Mazzoleni, G. Tortone, B. Velichkov:
Regularity of the optimal sets for a class of integral shape functionals
Arch. Rat. Mech. Anal. 2022
F. Générau, E. Oudet, B. Velichkov:
Numerical computation of the cut locus via a variational approximation of the distance function
ESAIM: M2AN 2022
L. Ferreri, B. Velichkov:
A one-sided two phase Bernoulli free boundary problem
(preprint) 2023
L. Ferreri, G. Tortone, B. Velichkov:
A capillarity one-phase Bernoulli free boundary problem
(preprint) 2023
N. Edelen, L. Spolaor, B. Velichkov:
The symmetric (log-)epiperimetric inequality and a decay-growth estimate
Calculus of Variations and Partial Differential Equations 2023
F. P. Maiale, G. Tortone, B. Velichkov:
Epsilon-regularity for the solutions of a free boundary system
Revista Matemática Iberoamericana 2023
L. Ferreri, B. Velichkov:
Regularity for one-phase Bernoulli problems with discontinuous weights and applications
Trans. Amer. Math. Soc. (Accepted Paper) 2023
L. Ferreri, L. Spolaor, B. Velichkov:
On the fine structure of the solutions to nonlinear thin two-membrane
problems in 2D
(preprint) 2024
L. Ferreri, L. Spolaor, B. Velichkov:
On the boundary branching set of the one-phase problem
(preprint) 2024
L. Ferreri, L. Spolaor, B. Velichkov:
Unique continuation for nonlinear variational problems
(preprint) 2024
R. Ognibene, B. Velichkov:
Boundary regularity of the free interface in spectral optimal partition
problems
(preprint) 2024
M. Carducci, B. Velichkov:
An epiperimetric inequality for odd frequencies in the thin obstacle
problem
(preprint) 2024
N. Edelen, L. Spolaor, B. Velichkov:
A strong maximum principle for minimizers of the one-phase Bernoulli problem
Indiana Univ. Math. J. 2024
G. De Philippis, L. Spolaor, B. Velichkov:
(Quasi-)conformal methods in two-dimensional free boundary problems
J. Eur. Math. Soc. 2024
G. Bevilacqua, S. Stuvard, B. Velichkov:
Classical solutions to the soap film capillarity problem for plane
boundaries
(preprint) 2024
F. P. Maiale, G. Tortone, B. Velichkov:
The boundary Harnack principle on optimal domains
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 2024
D. Mazzoleni, G. Tortone, B. Velichkov:
On the dimension of the singular set in optimization problems with measure constraint
J. Convex Analysis: volume dedicated to Giuseppe Buttazzo on the occasion of his 70th birthday. 2024