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 R. Ognibene, B. Velichkov: Boundary regularity of the free interface in spectral optimal partition problems (preprint) 2024