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SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1056 - 1084
We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann... 
Domain derivative | Duality | Shape functionals | Infimum problems | MATHEMATICS, APPLIED | CONVEXITY | domain derivative | POSITIVE SOLUTIONS | infimum problems | EQUATIONS | PRINCIPLE | shape functionals | duality | SOBOLEV SPACES | SYMMETRY | BOUNDED SLOPE CONDITION | REGULARITY | OPTIMIZATION | FUNCTIONALS | AUTOMATION & CONTROL SYSTEMS | Mathematics - Optimization and Control | Mathematics
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 10/2018, Volume 24, Issue 4, pp. 1585 - 1604
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider... 
First Dirichlet eigenvalue | Shape optimization | Torsional rigidity | MATHEMATICS, APPLIED | first Dirichlet eigenvalue | shape optimization | INEQUALITY | DOMAINS | AUTOMATION & CONTROL SYSTEMS | Eigenvalues | Lower bounds | Dirichlet problem | Convexity | Mathematical analysis | Torsion | Analysis of PDEs | Mathematics | Classical Analysis and ODEs
Journal Article
JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2015, Volume 22, Issue 2, pp. 303 - 338
In this paper we analyze the concentration phenomena which occur in thin rods, solving the following optimization problem: a given fraction of elastic material... 
MATHEMATICS | CHEEGER SETS | optimization | compliance | Thin rods | Cheeger problem | generalized Cheeger sets | duality | dimension reduction
Journal Article
Applied Mathematics Research eXpress, ISSN 1687-1200, 03/2017, Volume 2017, Issue 1, pp. 184 - 241
Abstract Given a bounded open set Ω⊂Rd with Lipschitz boundary and an increasing family Γt, t∈[0,T], of closed subsets of Ω, we analyze the scalar wave... 
Journal Article
Interfaces and Free Boundaries, ISSN 1463-9963, 2013, Volume 15, Issue 1, pp. 95 - 119
We study a 2d-variational problem, in which the cost functional is an integral depending on the gradient through a convex but not strictly convex integrand,... 
Free boundary problems | Convexity | Thin torsion rods | Cheeger sets | MATHEMATICS | MATHEMATICS, APPLIED | free boundary problems | DESIGN | CONVEX BODY | REGULARITY | thin torsion rods | PLATES | FLOW | UNIQUENESS
Journal Article
Applied Mathematics and Optimization, ISSN 0095-4616, 11/2017, Volume 79, Issue 3, pp. 1 - 26
We show that the compliance functional in elasticity is differentiable with respect to horizontal variations of the load term, when the latter is given by a... 
Shape derivatives | Sensitivity analysis | Transport theory | Elastical compliance | MATHEMATICS, APPLIED | Mathematics
Journal Article
Rivista di Matematica della Universita di Parma, ISSN 0035-6298, 2018, Volume 9, Issue 2, pp. 283 - 327
Journal Article
04/2020
In this paper we address the following shape optimization problem: find the planar domain of least area, among the sets with prescribed constant width and... 
Journal Article
10/2019
We study Blaschke-Santal\'o diagrams associated to the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work... 
Mathematics - Optimization and Control
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2012, Volume 44, Issue 1, pp. 483 - 512
We carry out an asymptotic analysis of the following shape optimization problem: a given volume fraction of elastic material must be distributed in a... 
Dimension reduction | Compliance | Thin rods | Duality | Cheeger sets | G-convergence | Optimization | MATHEMATICS, APPLIED | DESIGN | optimization | compliance | thin rods | PLATES | duality | dimension reduction | UNIQUENESS | Mathematics
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123656
In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed... 
Energy-dissipation balance | Wave equation in time-dependent domains | Fracture dynamics | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2018, Volume 25, Issue 5, pp. 1 - 28
In this work we first analyze the singular behavior of the displacement u of a linearly elastic body in dimension 2 close to the tip of a smooth crack,... 
Energy release rate | Stress intensity factor | Analysis | Brittle fracture | 74G40 | Mathematics | 35Q74 | 35B40 | 74R10 | 74G70 | FRACTURE | MATHEMATICS, APPLIED | MODEL
Journal Article
06/2019
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar... 
Mathematics - Analysis of PDEs
Journal Article
06/2018
In this paper we prove the following Kohler-Jobin type inequality: for any open, bounded set $\Omega \subset \mathbb R^N$ and any ball $\subset \mathbb R^N$ we... 
Mathematics - Analysis of PDEs
Journal Article
02/2017
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider... 
Mathematics - Analysis of PDEs
Journal Article
08/2018
The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The $\Gamma$-limit of a suitable rescaling of the... 
Mathematics - Analysis of PDEs
Journal Article
10/2016
A system of $n$ screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity. Imposing a suitable... 
Mathematics - Analysis of PDEs
Journal Article
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