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math.AP2025
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…
math.AP2025
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…
math.AP2025★ 1 cited
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}…