5 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 est…