Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Lucardesi, Ilaria"'
Autor:
Lucardesi, Ilaria, Zucco, Davide
The P\'al inequality is a classical result which asserts that among all planar convex sets of given width the equilateral triangle is the one of minimal area. In this paper we prove three quantitative versions of this inequality, by quantifying how t
Externí odkaz:
http://arxiv.org/abs/2405.18294
Autor:
Cavallina, Lorenzo, Funano, Kei, Henrot, Antoine, Lemenant, Antoine, Lucardesi, Ilaria, Sakaguchi, Shigeru
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{\mu_k(\Omega):\Omega \mbox{ convex},\Omega \subset D, \}$ (for a given box $D$) and $\max\{\mu_k(\Omega):\Om
Externí odkaz:
http://arxiv.org/abs/2312.13747
We study the Blaschke-Santal\'o diagram associated to the area, the perimeter, and the moment of inertia. We work in dimension 2, under two assumptions on the shapes: convexity and the presence of two orthogonal axis of symmetry. We discuss topologic
Externí odkaz:
http://arxiv.org/abs/2307.11658
In this paper we prove that among all convex domains of the plane with two axis of symmetry, the maximizer of the first non trivial Neumann eigenvalue $\mu_1$ with perimeter constraint is achieved by the square and the equilateral triangle. Part of t
Externí odkaz:
http://arxiv.org/abs/2210.17225
Autor:
Henrot, Antoine, Lucardesi, Ilaria
In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux po
Externí odkaz:
http://arxiv.org/abs/2011.07244
Autor:
Henrot, Antoine, Lucardesi, Ilaria
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:
http://arxiv.org/abs/2004.10865
Autor:
Lucardesi, Ilaria, Zucco, Davide
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -)
We study Blaschke-Santal\'o diagrams associated to the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work under convexity and volume constraints, in both strong (volume exactly one) and weak (volu
Externí odkaz:
http://arxiv.org/abs/1910.04454
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of (unions of
Externí odkaz:
http://arxiv.org/abs/1906.02631
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 smooth path. Moreover, we characterize the singularity of the displacement near the crack t
Externí odkaz:
http://arxiv.org/abs/1905.02498
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:
http://arxiv.org/abs/1808.08898