Antoine Lemenant

Maître de conférences

From now on I try to send all my papers to academic journals or independent journals in priority. Here is a list of academic journals selected by Michael Goldman.

List of publications/preprints

  • Self-contracted curves are gradient flows of convex functions
    (with Estibalitz Durand Cartagena) Preprint - Link

  • Stationarity of the crack-front for the Mumford-Shah problem in 3D
    (with Hayk Mikayelyan) Preprint - Link

  • On a phase field approximation of the planar Steiner problem: Existence, regularity, and asymptotic of minimizers
    (with M. Bonnivard and V. Millot) To appear in Interfaces and Free Boundaries - Link

  • Rectifiability of non Euclidean planar self-contracted curves
    Accepted in Confluentes Mathematici - 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

  • Phase Field models for thin elastic structures with topological constraint
    (With P. Dondl et S. Wojtowytsch), accepted in Arch. Ration. Mech. Anal. - 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

  • A Modica-Mortola approximation for the Steiner Problem.
    (With F. Santambrogio) Compt. Rend. Ac. Sci. Paris 352 (2014) - Link

  • On sets minimizing their weighted length in uniformly convex separable Banach spaces.
    (With T. De Pauw and V. Millot) accepted in Adv. Math. - 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

  • 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

  • On the extension property of Reifenberg-flat domains.
    (With E. Milakis and L. V. Spinolo) - Annales Academiae Scientiarum Fennicae Mathematica - 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) - Journal of Elasticity - 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

  • About the regularity of average distance minimizers in R^2.
    Journal of Convex Analysis 18 (2011), No. 4, 949--981. - 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

  • 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

  • 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


  • HDR- Régularité, stabilité, ou approximation d'un ensemble singulier intervenant en calcul des variations
    (2016) - HDR

  • Thèse Doctorat - Sur la régularité des minimiseurs de Mumford-Shah en dimension 3 et supérieure.
    Encadrée par Guy David (2008) - PDF

  • Mémoire de D.E.A. - Orsay, Août 2006 - encadrée par Guy David. On parle notamment de la fonctionnelle de Mumford-Shah et du théorème d'analycité des minimiseurs de Koch-Leoni-Morini utilisant un théorème un Morrey de 1966 sur les systèdmes elliptiques à poid pour résoudre une conjecture de De Giorgi. - PDF

  • Mémoire de Maîtrise - Introduction au front d'onde d'une distribution.
    Mémoire encadrée par Serge Alinhac (2003) à l'université d'Orsay Paris XI - PDF