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MAT102
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Free Boundary Problems
•
Regularity of the free boundary for the vectorial Bernoulli problem
(with
Dario Mazzoleni
and
Susanna Terracini
)
•
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
(with
Max Engelstein
and
Luca Spolaor
)
•
Direct epiperimetric inequalities for the thin obstacle problem and applications
(with
Maria Colombo
and
Luca Spolaor
)
•
A logarithmic epiperimetric inequality for the obstacle problem
(with
Maria Colombo
and
Luca Spolaor
, GAFA - Geom. Funct. Anal.)
•
An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case
(with
Luca Spolaor
, Comm. Pure Appl. Math.)
•
Regularity of the optimal sets for some spectral functionals
(with
Dario Mazzoleni
and
Susanna Terracini
, GAFA - Geom. Funct. Anal. 2017)
•
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
)
•
Existence and Regularity for Spectral Optimization Problems with Perimeter Constraint
(with
Guido De Philippis
,
Appl. Math. Optim. 2014
)
•
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)
Regularity of minimal surfaces
•
(Log-)Epiperimetric Inequality and Regularity over Smooth Cones for Almost Area-Minimizing Currents
(with
Max Engelstein
and
Luca Spolaor
)
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)
•
Multiphase Optimization Problems for Eigenvalues: Qualitative Properties and Numerical Results
(with
Beni Bogosel
, SIAM Numerical Analysis 2016)
•
Multiphase Shape Optimization Problems
(with
Dorin Bucur
,
SIAM J. Control Optim. 2014
)
Spectral and Shape Optimization Problems
•
Optimal potentials for problems with changing sign data
(with
Giuseppe Buttazzo
and Faustino Maestre, 2017)
•
A shape optimal control problem with changing sign data
(with
Giuseppe Buttazzo
, SIAM J. Math. Anal.)
•
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)
•
Shape Optimization Problems on Metric Measure Spaces
(with
Giuseppe Buttazzo
, J.Funct.Anal. 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)