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Free Boundary Problems

Regularity of minimizers of shape optimization problems involving perimeter

(with Guido De Philippis, Jimmy Lamboley and Michel Pierre, JMPA 2017)

A free boundary problem arising in PDE optimization

(with Giuseppe Buttazzo and Edouard Oudet, Calc.Var.PDE 2016)

Lipschitz Regularity of the Eigenfunctions on Optimal Domains

(with Dorin Bucur, Dario Mazzoleni and Aldo Pratelli, Arch. Rat. Mech. Anal. 2015)

A Note on the Monotonicity Formula of Caffarelli-Jerison-Kenig

(Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat.Appl. 2014)

Multiphase and Optimal Partition Problems

On the honeycomb conjecture for a class of minimal convex partitions (with Dorin Bucur, Ilaria Fragalà and Gianmaria Verzini, Transactions AMS 2017)

Spectral and Shape Optimization Problems

Worst-case shape optimization for the Dirichlet energy

(with J. C. Bellido and Giuseppe Buttazzo, Nonlinear Analysis 2016)

Spectral Optimization Problems for Potentials and Measures

(with Dorin Bucur and Giuseppe Buttazzo, SIAM J. Math. Anal. 2014)

Optimal Potentials for Schrodinger Operators (with Giuseppe Buttazzo, Augusto Gerolin and Berardo Ruffini, Journal de l'École polytechnique — Mathématiques 2014)

Shape Optimization Problems for Metric Graphs

(with Giuseppe Buttazzo and Berardo Ruffini, ESAIM: COCV 2014)

Spectral Optimization Problems with Internal Constraint

(with Dorin Bucur and Giuseppe Buttazzo, Ann.Inst.H.P. 2013)

Further topics in Calculus of Variations and PDE

Numerical Calibration of Steiner trees

(with Annalisa Massaccesi and Edouard Oudet, Appl. Math. Optim. 2017)

BV estimates in optimal transportation and applications

(with Guido De Philippis, Alpar Meszaros and Filippo Santambrogio, ARMA 2015)

Faber-Krahn inequalities in sharp quantitative form

(with Lorenzo Brasco and Guido De Philippis, Duke Math. J. 2015)

Review articles, proceedings and book chapters

Spectral optimization problems for Schrödinger operators (with Giuseppe Buttazzo, Chapter 9 from the book Shape Optimization and Spectral Theory, De Gruyter 2017)

The spectral drop problem
(with Giuseppe Buttazzo, Contemporary mathematics 666, 2016)

A free boundary approach to shape optimization problems

(with Dorin Bucur, Philosophical Transactions of the Royal Society of London A 2015)

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity (with Giuseppe Buttazzo and Michiel van den Berg, Chapter from the book New Trends in Shape Optimization 2015)

Some New Problems in Spectral Optimization

(with Giuseppe Buttazzo, Banach Center Publications 2014)