Shape derivatives for minima of integral functionals

Autor: Guy, Bouchitte, Ilaria, Fragala, Ilaria, Lucardesi

For $\Omega$ varying among open bounded sets in ${\mathbb R} ^n$, we consider shape functionals $J (\Omega)$ defined as the infimum over a Sobolev space of an integral energy of the kind $\int _\Omega[ f (\nabla u) + g (u) ]$, under Dirichlet or Neum

Externí odkaz: http://arxiv.org/abs/1401.2788

Shape Sensitivity Analysis of a 2D Fluid–Structure Interaction Problem

Autor: Valentin Calisti, Ilaria Lucardesi, Jean-François Scheid

Publikováno v: Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications, In press, pp.1-33. ⟨10.1007/s10957-023-02213-4⟩

We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes–elasticity system with small loads, with respect to the reference domain of the elastic structure immersed in a viscous flui

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55952ea9df72529e7004e61517287f0d
https://doi.org/10.1007/s10957-023-02213-4

BODY OF CONSTANT WIDTH WITH MINIMAL AREA IN A GIVEN ANNULUS

Autor: Antoine Henrot, Ilaria Lucardesi

Publikováno v: Journal de l'École polytechnique — Mathématiques
Journal de l'École polytechnique — Mathématiques, École polytechnique, In press

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 inradius. In the literature, the problem is ascribed to Bonnesen, who proposed it in \cite{BF}.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::16aa5ab16c97042bf610ab72fcde9405
https://hal.archives-ouvertes.fr/hal-02551415

Upscaling of screw dislocations with increasing tangential strain

Autor: Marco Morandotti, Davide Zucco, Riccardo Scala, Ilaria Lucardesi

Publikováno v: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni, European Mathematical Society, 2020, 31 (2), pp.421-445. ⟨10.4171/RLM/898⟩
Rendiconti Lincei. Matematica e Applicazioni
Rendiconti Lincei. Matematica e Applicazioni, European Mathematical Society, 2020, 31 (2), pp.421-445. ⟨10.4171/RLM/898⟩

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 renormalized energy is characterized in the space of probability measures. This corresponds to a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b76c469ddb83ec1ba8b0c7ac31446fd3
https://hal.archives-ouvertes.fr/hal-02893723

Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint

Autor: Beniamin Bogosel, Antoine Henrot, Ilaria Lucardesi

Publikováno v: SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, 50 (5), pp.5337-5361. ⟨10.1137/17M1162147⟩

International audience; In this paper we look for the domains minimizing the h-th eigenvalue of the Dirichlet-Laplacian λ h with a constraint on the diameter. Existence of an optimal domain is easily obtained, and is attained at a constant width bod

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94a9060ff8bafa1cc88aabcc4672d5f1
https://doi.org/10.1137/17m1162147