44 citations · 84 across the 29 of their papers we have counts for
24 papers · 1 filter
Good access to the crack and integrability of the full gradient for Griffith almost-minimizers in the plane
Camille Labourie, Lorenzo Lamberti, Antoine Lemenant
We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement sa…
Finite number of traces for Mumford-Shah minimizers in dimension 2
Camille Labourie, Antoine Lemenant
In this short note, we answer a question raised by E. De Giorgi, showing that a Mumford-Shah minimizer in dimension 2 can only admit three maximum limit values as approaching the s…
A field-road system with a rectifiable set
Matthieu Bonnivard, Romain Ducasse, Antoine Lemenant +1
The aim of this paper is to define a field-road system in 2D where the road is a merely 1D-rectifiable set. For this purpose we introduce a general setting in order to define a par…
Boundary regularity for the polyharmonic Dirichlet problem
Antoine Lemenant, Rémy Mougenot
In this paper we prove that any solution of the -polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is $\mathscr{C}^{m-1,α}…
Minimization of the first eigenvalue for the Lamé system
Antoine Henrot, Antoine Lemenant, Yannick Privat
In this article, we address the problem of determining a domain in that minimizes the first eigenvalue of the Lamé system under a volume constraint. We begin by esta…
The biharmonic optimal support problem
Antoine Lemenant, Mohammad Reza Pakzad
We establish a -convergence result for of a thin nonlinearly elastic 3D-plate of thickness which is assumed to be glued to a support region in the 2D-plane $x_3=0…
Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
Pablo Àlvarez-Caudevilla, Matthieu Bonnivard, Antoine Lemenant
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…
Epsilon-regularity for Griffith almost-minimizers in any dimension under a separating condition
Camille Labourie, Antoine Lemenant
In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is -close to a plane in some ball B R N while separating the ball B in tw…
An isoperimetric problem with two distinct solutions
Antoine Henrot, Antoine Lemenant, Ilaria Lucardesi
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 with perimeter constrai…
Regularity improvement for the minimizers of the two-dimensional Griffith energy
Camille Labourie, Antoine Lemenant
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 inte…
Partial regularity for the crack set minimizing the two-dimensional Griffith energy
Jean-François Babadjian, Flaviana Iurlano, Antoine Lemenant
In this paper we prove a regularity result for minimizers of the planar Griffith functional arising from a variational model of brittle fracture. We prove that a…
Self-contracted curves are gradient flows of convex functions
Antoine Lemenant, Estibalitz Durand Cartagena
In this paper we prove that any curve in , with , is the solution of the gradient flow equation for some convex function , if…
Stationarity of the crack-front for the Mumford-Shah problem in 3D
Antoine Lemenant, Hayk Mikayelyan
In this paper we exhibit a family of stationary solutions of the Mumford-Shah functional in , arbitrary close to a crack-front. Unlike other examples, known in the li…
On a phase field approximation of the planar Steiner problem: existence, regularity, and asymptotic of minimizers
Matthieu Bonnivard, Antoine Lemenant, Vincent Millot
In this article, we consider and analyse a small variant of a functional originally introduced in \cite{BLS,LS} to approximate the (geometric) planar Steiner problem. This function…
Phase field models for thin elastic structures with topological constraint
Patrick W. Dondl, Antoine Lemenant, Stephan Wojtowytsch
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container.…
Energy release rate for non smooth cracks in planar elasticity
Jean-François Babadjian, Antonin Chambolle, Antoine Lemenant
This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density at the tip. First, the blow-up limit o…
A rigidity result for global Mumford-Shah minimizers in dimension three
Antoine Lemenant
We study global Mumford-Shah minimizers in , introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of when…
A Modica-Mortola approximation for the Steiner Problem
Antoine Lemenant, Filippo Santambrogio
In this note we present a way to approximate the Steiner problem by a family of elliptic energies of Modica-Mortola type, with an additional term relying on the weighted geodesic d…
Boundary regularity for the Poisson equation in reifenberg-flat domains
Antoine Lemenant, Yannick Sire
This paper is devoted to the investigation of the boundary regularity for the Poisson equation $${{cc} -Δu = f & \text{in} Ω u= 0 & \text{on} \partial Ω$$ where belongs to some…
On the extension property of Reifenberg-flat domains
Antoine Lemenant, Emmanouil Milakis, Laura V. Spinolo
We provide a detailed proof of the fact that any domain which is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it is an extension domain. We discuss va…
Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains
Antoine Lemenant, Emmanouil Milakis, Laura V. Spinolo
In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our ma…
On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
Antoine Lemenant
We show that if is a global minimizer for the Mumford-Shah functional in , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degr…
Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone
Antoine Lemenant
We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R^3, and if x, K and r > 0 are such that K is close enough to a minimal cone of type P (a plan…
Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets
Antoine Lemenant
Let P be an hyperplane in R^N, and denote by dH the Hausdorff distance. We show that for all positive radius r < 1 there is an epsilon > 0, such that if K is a Reifenberg-flat set…