D. Bucur, G. Buttazzo, P. Trebeschi: An Existence Result for Optimal Obstacles () 1998 D. Bucur, G. Buttazzo: Results and Questions on Minimum Problems for Eigenvalues () 1998 D. Bucur, P. Trebeschi: Shape Optimization Problems Governed by Nonlinear State Equations () 1998 D. Bucur, G. Buttazzo, N. Varchon: On the problem of optimal cutting SIAM J. Optim. 2001 Z. Belhachmi, D. Bucur, G. Buttazzo, J. M. Sac-Epée: Shape optimization problems for eigenvalues of elliptic operators (Preprint) 2005 D. Bucur, G. Buttazzo, A. Lux: Quasistatic evolution in debonding problems via capacitary methods (Submitted Paper) 2006 D. Bucur, G. Buttazzo: Irreversible quasistatic evolutions by minimizing movements (Preprint) 2007 D. Bucur, G. Buttazzo, A. Henrot: Minimization of $\lambda_2(\Omega)$ with a perimeter constraint (Preprint) 2009 D. Bucur, A. Giacomini: A variational approach to the isoperimetric inequality for the Robin eigenvalue problem Arch. Ration. Mech. Anal. Vol. 198, p. 927-961, 2010 D. Bucur: Minimization of the k-th eigenvalue of the Dirichlet Laplacian Arch. Ration. Mech. Anal. Vol. 206 , p. 1073-1083, 2012 D. Bucur, I. Fragalà, J. Lamboley: Optimal convex shapes for concave functionals ESAIM Control Optim. Calc. Var. Vol. 18, N. 3, p. 693-711, 2012 D. Bucur, G. Buttazzo: On the characterization of the compact embedding of Sobolev spaces Calc. Var. and PDEs (Accepted Paper) p. 19, 2012 D. Bucur, S. Luckhaus: Monotonicity formula and regularity for general free discontinuity problems ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (Accepted Paper) 2013 D. Bucur, G. Buttazzo, U. Stefanelli: Shape flows for spectral optimization problems Interfaces Free Bound. Vol. 14, p. 521--544, 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 D. Bucur, I. Fragalà: A Faber-Krahn inequality for the Cheeger constant of N-gons Journal of Geometric Analysis (Submitted Paper) 2014 D. Bucur, G. Buttazzo, B. Velichkov: Spectral optimization problems for potentials and measures SIAM J. Math. Anal. 2014 D. Bucur, B. Velichkov: Multiphase shape optimization problems SIAM J. Control Optim. 2014 D. Bucur, D. Mazzoleni: A surgery result for the spectrum of the Dirichlet Laplacian SIAM J. Math. Anal. Vol. 47, N. 6, p. 4451-4466, 2015 D. Bucur, A. Giacomini: FABER-KRAHN INEQUALITIES FOR THE ROBIN-LAPLACIAN: A FREE DISCONTINUITY APPROACH Arch. Ration. Mech. Anal. Vol. 218, p. 757-824, 2015 D. Bucur, A. Giacomini: Shape optimization problems with Robin conditions on the free boundary Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2015 D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov: Lipschitz regularity of the eigenfunctions on optimal domains Arch. Rat. Mech. Anal. 2015 B. Bogosel, D. Bucur, A. Giacomini: Optimal shapes maximizing the Steklov eigenvalues (SIAM J. Math. Analysis (to appear)) 2016 D. Bucur, A. Giacomini, P. Trebeschi: The Robin-Laplacian problem on varying domains Calc. Var. Partial Differential Equations Vol. 55, p. 55-133, 2016 D. Bucur, A. Giacomini: Minimization of the k-th eigenvalue of the Robin-Laplacian (Preprint) 2017 D. Bucur, I. Fragalà: On the honeycomb conjecture for Robin Laplacian eigenvalues (Preprint) 2017 B. Bogosel, D. Bucur, I. Fragalà: Phase field approach to optimal packing problems and related Cheeger clusters (Submitted Paper) 2017 D. Bucur, A. Giacomini, P. Trebeschi: Best constant in Poincaré inequalities with traces: a free discontinuity approach (Submitted Paper) 2017 D. Bucur, I. Fragalà: Proof of the honeycomb asymptotics for optimal Cheeger clusters (Submitted Paper) 2017 D. Bucur, G. Buttazzo, C. Nitsch: Two optimization problems in thermal insulation Notices Amer. Math. Soc. Vol. 64, N. 8, p. 830-835, 2017 D. Bucur, V. Ferone, C. Nitsch, C. Trombetti: Weinstock inequality in higher dimensions (Submitted Paper) 2017 D. Bucur, A. Henrot: A new isoperimetric inequality for the elasticae JEMS (Accepted Paper) 2017 D. Bucur, G. Buttazzo, C. Nitsch: Symmetry breaking for a problem in optimal insulation Journal de Mathématiques Pures et Appliquées (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 D. Bucur, A. Henrot: Maximization of the second non-trivial Neumann eigenvalue (Submitted Paper) 2018 D. Bucur, I. Fragalà, A. Giacomini: Optimal partitions for Robin Laplacian eigenvalues (preprint) 2018 D. Bucur, M. van den Berg: Sign changing solutions of Poisson's equation (preprint) 2018 D. Bucur, I. Fragalà, A. Giacomini: Local minimality results for the Mumford-Shah functional via monotonicity (Submitted Paper) 2018 D. Bucur, I. Fragalà, A. Giacomini: Multiphase Free Discontinuity Problems: Monotonicity Formula and Regularity Results (Submitted Paper) 2018 D. Bucur, I. Fragalà, A. Giacomini: The Multiphase Mumford-Shah Problem (Submitted Paper) 2019 D. Bucur, A. Giacomini, P. Trebeschi: $L^\infty$ bounds of Steklov eigenfunctions and spectrum stability under domain variation (Submitted Paper) 2019 D. Bucur, S. Cito: Geometric control of the Robin Laplacian eigenvalues: the case of negative boundary parameter Journal of Geometric Analysis 2019 D. Bucur, M. Nahon: Stability and instability issues of the Weinstock inequality (Submitted Paper) 2020 D. Bucur, I. Fragalà: Symmetry results for variational energies on convex polygons (Submitted Paper) 2020 D. Bucur, A. Giacomini, M. Nahon: Degenerate free discontinuity problems and spectral inequalities in quantitative form (Submitted Paper) 2020 D. Bucur, I. Fragalà: Rigidity for measurable sets (preprint) 2021 D. Bucur, M. Nahon, C. Nitsch, C. Trombetti: Shape optimization of a thermal insulation problem (preprint) 2021 D. Bucur, A. Giacomini, P. Trebeschi: Stability results for the Robin Laplacian on nonsmooth domains (Submitted Paper) 2021 D. Bucur, A. Henrot, M. Michetti: Asymptotic behaviour of the Steklov problem on dumbbell domains Comm. Partial Differential Equations Vol. 46, N. 2, p. 362-393, 2021 B. Bogosel, D. Bucur: On the Polygonal Faber-Krahn Inequality (Preprint) 2022 D. Bucur, E. Martinet, E. Oudet: Maximization of Neumann eigenvalues (Submitted Paper) 2022 D. Bucur, E. Martinet, M. Nahon: Sharp inequalities for Neumann eigenvalues on the sphere (Submitted Paper) 2022 L. Briani, D. Bucur: Mean-to-max ratio of the torsion function and honeycomb structures (Preprint) 2023 D. Bucur, A. Chambolle, A. Giacomini, M. Nahon: A free discontinuity approach to optimal profiles in Stokes flows (preprint) 2023 B. Bogosel, D. Bucur, I. Fragalà: The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities (preprint) 2023 D. Bucur, J. Lamboley, M. Nahon, R. Prunier: Sharp Quantitative Stability of the Dirichlet spectrum near the ball (preprint) 2023 V. Amato, D. Bucur, I. Fragalà: The geometric size of the fundamental gap (Submitted Paper) 2024