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# Documents  Pratelli, Aldo | enregistrements trouvés : 7

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## Some new inequalities for the Cheeger constant Fragalà, Ilaria | CIRM H

Post-edited

Research talks;Control Theory and Optimization;Partial Differential Equations;Geometry

We discuss some new results for the Cheeger constant in dimension two, including:
- a polygonal version of Faber-Krahn inequality;
- a reverse isoperimetric inequality for convex bodies;
- a Mahler-type inequality in the axisymmetric setting;
- asymptotic behaviour of optimal partition problems.
Based on some recent joint works with D.Bucur,
and for the last part also with B.Velichkov and G.Verzini.

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## New trends in shape optimization.Based on a workshop held at the Friedrich-Alexander University Erlangen-NürnbergErlangen # September 2013 Pratelli, Aldo ; Leugering, Günter | Birkhäuser 2015

Congrès

- viii; 314 p.
ISBN 978-3-319-17562-1

International series of numerical mathematics , 0166

Localisation : Colloque 1er étage (ERLA)

optimisation de forme # thermodynamique # variable d'état # équation d'état # problème de minimisation # problème de Cheeger # espace métrique # topologie # gradient de forme # méthode de Lagrange-Newton # PDE sous contrainte # application électromagnétique # opérateur Laplacien

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## Regularity of the optimal sets for spectral functionals. Part I: sum of eigenvalues Terracini, Susanna | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Partial Differential Equations

In this talk we deal with the regularity of optimal sets for a shape optimization problem involving a combination
of eigenvalues, under a fixed volume constraints. As a model problem, consider
$\min\Big\{\lambda_1(\Omega)+\dots+\lambda_k(\Omega)\ :\ \Omega\subset\mathbb{R}^d,\ \text{open}\ ,\ |\Omega|=1\Big\},$
where $\langle_i(\cdot)$ denotes the eigenvalues of the Dirichlet Laplacian and $|\cdot|$ the $d$-dimensional Lebesgue measure.
We prove that any minimizer $_{opt}$ has a regular part of the topological boundary which is relatively open and
$C^{\infty}$ and that the singular part has Hausdorff dimension smaller than $d-d^*$, where $d^*\geq 5$ is the minimal
dimension allowing the existence of minimal conic solutions to the blow-up problem.

We mainly use techniques from the theory of free boundary problems, which have to be properly extended to the case of
vector-valued functions: nondegeneracy property, Weiss-like monotonicity formulas with area term; finally through the
properties of non tangentially accessible domains we shall be in a position to exploit the ''viscosity'' approach recently proposed by De Silva.

This is a joint work with Dario Mazzoleni and Bozhidar Velichkov.
In this talk we deal with the regularity of optimal sets for a shape optimization problem involving a combination
of eigenvalues, under a fixed volume constraints. As a model problem, consider
$\min\Big\{\lambda_1(\Omega)+\dots+\lambda_k(\Omega)\ :\ \Omega\subset\mathbb{R}^d,\ \text{open}\ ,\ |\Omega|=1\Big\},$
where $\langle_i(\cdot)$ denotes the eigenvalues of the Dirichlet Laplacian and $|\cdot|$ the $d$-dimensional Lebesgue m...

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## On the stability of the Bossel-Daners inequality Trombetti, Cristina | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Partial Differential Equations

The Bossel-Daners is a Faber-Krahn type inequality for the first Laplacian eigenvalue with Robin boundary conditions. We prove a stability result for such inequality.

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## A minimaxmax problem for improving the torsional stability of rectangular plates Gazzola, Filippo | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Partial Differential Equations;Mathematical Physics

We introduce a new function which measures the torsional instability of a partially hinged rectangular plate. By exploiting it, we compare the torsional performances of different plates reinforced with stiffening trusses. This naturally leads to a shape optimization problem which can be set up through a minimaxmax procedure.

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## Isoperimetry with density Morgan, Frank | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Geometry

In 2015 Chambers proved the Log-convex Density Conjecture, which says that for a radial density f on $R^n$, spheres about the origin are isoperimetric if and only if log f is convex (the stability condition). We discuss recent progress and open questions for other densities, unequal perimeter and volume densities, and other metrics.

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## Optimal urban networks via mass transportation Buttazzo, Giuseppe ; Pratelli, Aldo ; Solimini, Sergio ; Stepanov, Eugene | Springer-Verlag 2009

Ouvrage

- x; 150 p.
ISBN 978-3-540-85798-3

Lecture notes in mathematics , 1961

Localisation : Collection 1er étage

optimisation # équation de transport # réseau # flux en réseau # semi-continuité # convergence # mesure géométrique # traffic autoroutier

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