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) http://arxiv.org/abs/2107.12485 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 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) http://arxiv.org/abs/2309.01749 2023 L. Ferreri, G. Tortone, B. Velichkov: A capillarity one-phase Bernoulli free boundary problem (preprint) http://arxiv.org/abs/2310.14309 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) http://arxiv.org/abs/2309.09283 2023 L. Ferreri, L. Spolaor, B. Velichkov: On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D (preprint) http://arxiv.org/abs/2405.05799 2024 L. Ferreri, L. Spolaor, B. Velichkov: On the boundary branching set of the one-phase problem (preprint) http://arxiv.org/abs/2407.15230 2024 L. Ferreri, L. Spolaor, B. Velichkov: Unique continuation for nonlinear variational problems (preprint) http://arxiv.org/abs/2408.00405 2024 R. Ognibene, B. Velichkov: Boundary regularity of the free interface in spectral optimal partition problems (preprint) http://arxiv.org/abs/2404.05698 2024 M. Carducci, B. Velichkov: An epiperimetric inequality for odd frequencies in the thin obstacle problem (preprint) http://arxiv.org/abs/2409.12110 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) http://arxiv.org/abs/2407.09193 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 R. Ognibene, B. Velichkov: Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems (Preprint) 2024 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. 2024 M. Carducci, B. Velichkov: Existence and regularity in the fully nonlinear one-phase free boundary problem (preprint) http://arxiv.org/abs/2501.12101 2025 C. Gasparetto, F. Paiano, B. Velichkov: Regularity for free boundary surfaces minimizing degenerate area functionals (preprint) http://arxiv.org/abs/2503.02535 2025 A. Pacati, G. Tortone, B. Velichkov: Some remarks on singular capillary cones with free boundary (preprint) http://arxiv.org/abs/2502.07697 2025