Publications – Antoine Lemenant

The biharmonic optimal support problem (with R. Pakzad) – preprint (2024) – Link
Two extremum problems for Neumann eigenvalues (with L. Cavallina – K. Funano – A. Henrot – I. Lucardesi – S. Sakaguchi) – preprint (2023) – Link
Uniform concentration property for Griffith almost-minimizers (with C. Labourie) – preprint (2023) – Link

Stable domains for higher order elliptic operatorsn (with J-F. Grosjean and R. Mougenot) – CRAS accepté (2024) – Link

Epsilon-Regularity for Griffith almost-minimizers in any dimension under a separating condition (with C. Labourie) – Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 105, 63 p. (2023). – Link
An isoperimetric problem with two distinct solutions (with A. Henrot and I. Lucardesi) – Transactions of the AMS (accepted 2023) – Link

Regularity improvement for the minimizers of the two-dimensional Griffith energy (with C. Labourie) – accepted in Rendiconti Lincei Matematica e Applicazioni (2022) – Link
Partial regularity for the crack set minimizing the two-dimensional Griffith energy (with J. F. Babadjian and F. Iurlano) – JEMS (2022) – Link

Regularity for the planar optimal p-compliance problem (with B. Bulanyi) – ESAIM Control Optim. Calc. Var. (2021) – Link

Numerical approximation of the Steiner problem in dimension 2 and 3 (with M. Bonnivard and E. Bretin) Math. Comp. 89 (2020), no. 321, 1–43. – Link

Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials (with P. Alvarez-Caudevilla and M. Bonnivard) ESAIM COCV (2019) – Link

Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials (with P. Alvarez-Caudevilla and M. Bonnivard) ESAIM COCV (2019) – Link
Self-contracted curves are gradient flows of convex functions (with Estibalitz Durand Cartagena) Proc. Amer. Math. Soc. 147 (2019), no. 6, 2517–2531. – Link

Stationarity of the crack-front for the Mumford-Shah problem in 3D (with Hayk Mikayelyan) J. Math. Anal. Appl. 462 (2018) – Link
On a phase field approximation of the planar Steiner problem: Existence, regularity, and asymptotic of minimizers (with M. Bonnivard and V. Millot) Interfaces Free Bound. 20 (2018) – Link

Phase Field models for thin elastic structures with topological constraint (With P. Dondl et S. Wojtowytsch), Arch. Ration. Mech. Anal. 223 (2017), – Link
On sets minimizing their weighted length in uniformly convex separable Banach spaces. (With T. De Pauw and V. Millot) Adv. Math. 305, 1268-1319 (2017). – Link

Rectifiability of non Euclidean planar self-contracted curves Confluentes Math. 8 (2016) – Link
Regularity for the optimal compliance problem with length penalization (With A. Chambolle, J. Lamboley et E. Stepanov) , SIAM J. Math. Anal Vol. 49, No. 2, pp. 1166-1224 – Link
A selective review on Mumford-Shah minimizers. (Review paper) Boll. Unione Mat. Ital. 9 (2016) – Link

Energy release rate for non smooth cracks in planar elasticity. (With J-F. Babadjian and A. Chambolle) J. Ec. polytech. Math. 2 (2015) Link
A rigidity result for global Mumford-Shah minimizers in dimension three. J. Math. Pures Appl. (9) 103 (2015), no. 4 – Link
Approximation of length minimization problems among compact connected sets. (With M. Bonnivard and F. Santambrogio) SIAM J. Math. Anal. 47 (2015) – Link
Rectifiability of Self-contracted curves in the euclidean space and applications. (With A. Daniilidis, G. David and E. Durand-Cartagena) J. Geom. Anal. 25 (2015) – Link

A Modica-Mortola approximation for the Steiner Problem. (With F. Santambrogio) Compt. Rend. Ac. Sci. Paris 352 (2014) – Link
On the extension property of Reifenberg-flat domains. (With E. Milakis and L. V. Spinolo) – Ann. Acad. Sci. Fenn., Math. 39, No. 1, 51-71 (2014). – Link

Boundary regularity for the Poisson equation in reifenberg-flat domains. (With Y. Sire) Geometric partial differential equations, 189–209, CRM Series, 15, Ed. Norm., Pisa, (2013). – Link
Spectral Stability Estimates for the Dirichlet and Neumann Laplacian in rough domains. (With E. Milakis and L. V. Spinolo) J. Funct. Anal. 264 (2013), no. 9, 2097-2135. –Link
The stress intensity factor for non-smooth fractures in antiplane elasticiy. (With A. Chambolle) – Calc. Var. Partial Differential Equation 47 (2013), no. 3-4, 589-610. Link

Un théorème de régularité pour les minimiseurs de Mumford-Shah dans R^3. Compte rendu du séminaire X-EDP (proceeding)
On convex sets that minimize the average distance. (With E. Mainini) – ESAIM: COCV (2012) Link
A presentation of the average distance minimization problem. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 390 (2011) translation in J. Math. Sci. (N.Y.) 181 (2012), no. 6, 820-836 Link

A variational model for plastic slip and its regularization via Gamma-convergence. (With L. Ambrosio and G. Royer-Carfagni) – J. Elasticity 110, No. 2, 201-235 (2013).- Link
About the regularity of average distance minimizers in R^2. Journal of Convex Analysis 18 (2011), No. 4, 949–981. – Link
A stability result for nonlinear Neumann problems in Reifenberg flat domains in R^n. (With E. Milakis) – Publ. Mat. 55 (2011), 413-432 – Link
Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. X (2011), 561-609 – Link

Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence. (With P. Alvarez-Caudevilla) – Adv. in Diff. Eq. Vol. 15, 7-8 (2010), 649-688 – Link
Some stability results under domain variation for Neumann problems in metric spaces. (With E. Durand-Cartagena) – Ann. Ac. Sci. Fen. Math. Vol 35, (2010) – Link
Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in R^n. (With E. Milakis) – J. Math. Anal. Appl. 364 (2010) – Link
Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets. – Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010), 1-34 – Link

On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone. Rend. Semin. Mat. Univ. Padova 122, 129-159 (2009). – Link