Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Lemenant, Antoine"'
We establish a $\Gamma$-convergence result for $h\to 0$ of a thin nonlinearly elastic 3D-plate of thickness $h>0$ which is assumed to be glued to a support region in the 2D-plane $x_3=0$ over the $h$-2D-neighborhood of a given closed set $K$. In the
Externí odkaz:
http://arxiv.org/abs/2404.00689
Publikováno v:
ESAIM: COCV, Volume 26, 2020, Article Number: 50, Published online: 03 September 2020
In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a paraboli
Externí odkaz:
http://arxiv.org/abs/2401.14249
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
This paper is devoted to prove that any domain satisfying a $(\delta_0,r_0)-$capacity condition of first order is automatically $(m,p)-$stable for all $m\geqslant 1$ and $p\geqslant 1$, and for any dimension $N\geqslant 1$. In particular, this includ
Externí odkaz:
http://arxiv.org/abs/2307.07217
Autor:
Labourie, Camille, Lemenant, Antoine
Publikováno v:
Arch Rational Mech Anal 247, 105 (2023)
In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is $\epsilon$-close to a plane in some ball B $\subset$ R N while separating the ball B in two big parts, then K is C 1,$\alpha$ in a slightly smaller ball.
Externí odkaz:
http://arxiv.org/abs/2211.16180
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:
Labourie, Camille, Lemenant, Antoine
Publikováno v:
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (2023)
In this paper we prove that the singular set of connected minimizers of the planar Griffith functional has Hausdorff dimension strictly less then one, together with the higher integrability of the symetrized gradient.
Comment: Minor corrections
Comment: Minor corrections
Externí odkaz:
http://arxiv.org/abs/2111.13081
Autor:
Bulanyi, Bohdan, Lemenant, Antoine
In this paper we prove a partial $C^{1,\alpha}$ regularity result in dimension $N=2$ for the optimal $p$-compliance problem, extending for $p\not = 2$ some of the results obtained by A. Chambolle, J. Lamboley, A. Lemenant, E. Stepanov (2017). Because
Externí odkaz:
http://arxiv.org/abs/1911.09240
In this paper we prove a $\mathcal C^{1,\alpha}$ regularity result for minimizers of the planar Griffith functional arising from a variational model of brittle fracture. We prove that any isolated connected component of the crack, the singular set of
Externí odkaz:
http://arxiv.org/abs/1905.10298
In this paper we prove that any $C^{1,\alpha}$ curve in $\mathbb{R}^n$, with $\alpha \in (\frac{1}{2},1]$, is the solution of the gradient flow equation for some $C^1$ convex function $f$, if and only if it is strongly self-contracted.
Externí odkaz:
http://arxiv.org/abs/1802.07542