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 various …

This is a review paper on the Mumford-Shah functional, with particular interest in blow-up
limits, low dimensions (2 and 3), and connection with fracture theory. It includes in particular …

In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is ε-
close to a plane in some ball B⊂ RN while separating the ball B in two big parts, then K is C …

We present regularity results for the crack set of a minimizer for the Griffith fracture energy,
arising in the variational modeling of brittle materials. In the planar setting, we prove an …

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 …

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 …

We prove that if (u, K) is a minimizer of the Mumford-Shah functional in an open set of R3,
and if x∈ K and r> 0 are such that K is close enough to a minimal cone of type P (a plane), Y …

Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we
investigate the asymptotic behavior of the energy of the solution u of a Neumann problem …

In this paper we prove that if Ω and Ω′ are close enough for the complementary Hausdorff
distance and their boundaries satisfy some geometrical and topological conditions then …

Introduction Page 1 Publ. Mat. 55 (2011), 413–432 A STABILITY RESULT FOR NONLINEAR
NEUMANN PROBLEMS IN REIFENBERG FLAT DOMAINS IN RN Antoine Lemenant and …