HENROT Antoine

Position Full professor
Teaching department
Mines Nancy
Research group Partial Differential Equations
Research fields
  • Shape optimization
  • Spectral Geometry
  • Convex Geometry
  • Analysis of Partial Differential Equations
  • Free Boundary Problems
Mail

IECL – Site de Nancy
Faculté des sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy

Email antoine.henrot@univ-lorraine.fr
Phone number 03 72 74 54 07 or 03 72 74 49 35
Office 222 (ou R421 à l'école des Mines)

Welcome on my webpage

If you want to join me, the best is to write an email. I will generally answer the same day.

In the “Research” tab, you will find the list of my publications with a link to  Arxiv or HAL in many cases.

 


Articles parus ou acceptés dans
des Revues Internationales à Comité de Lecture

  1. “Un problème inverse en formage des métaux liquides”, en collaboration avec Michel Pierre, in Modél. Math. et Anal. Num., vol.23, n. 1, 1989, p. 155-177.
  2. “About existence of equilibria in lectromagnetic casting”, en collaboration avec Michel Pierre, in Quarterly of Applied Math., vol. 49. n. 3, 1991, p. 563-575.
  3. “A nonlinear boundary value problem solved by spectral methods”, en collaboration avec Olivier Coulaud, in Applicable Analysis, vol. 43, 1992, p. 229-244.
  4. “Behaviour of the free boundary in electromagnetic shaping when the surface tension vanishes”, in Nonlinear Analysis T.M.A., vol. 20, n. 8, 1993, p. 965-978.
  5. “Numerical approximation of a free boundary problem arising in electromagnetic shaping”, en collaboration avec Olivier Coulaud, in SIAM J. of Numerical Analysis, vol. 31, n. 4, 1994, p. 1109-1127.
  6. “Subsolutions and supersolutions in a free boundary problem”, in Arkiv för Matematik, vol. 32, 1994, p. 79-98.
  7. “Continuity with respect to the domain for the laplacian: a survey”, in Control and Cybernetics, vol. 23, n. 3, 1994, p. 427-443.
  8. “Domain optimization problem for stationary heat equation”, en collaboration avec W. Horn et Jan Sokolowski, in Appl. Math. and Comp. Sci., vol.6, No.2, 1996, p. 1-21.
  9. “How to prove symmetry in shape optimization problems?”, in Control and Cybernetics, vol. 25, n.5, 1996, p. 1001-1013.
  10. “Convexity of free boundaries with Bernoulli type boundary condition”, en collaboration avec Henrik Shahgholian, in Nonlinear Analysis T.M.A., vol. 28, n. 5, 1997, p. 815-823..
  11. “On a class of overdetermined eigenvalue problems”, en collaboration avec Gérard A. Philippin, in Mathematical Methods in the Applied Sciences, vol. 20, 1997, p. 905-914.
  12. “Un résultat d’existence en optimisation de forme en utilisant une propriété géométrique de la normale”, en collaboration avec Mohamed Barkatou, in ESAIM COCV, vol. 2, 1997, p. 105-123.
  13. “Use of domain derivative to prove symmetry results in partial differential equations”, en collaboration avec Mourad Choulli,in Mathematische Nachrichten, vol. 192, 1998, p. 91-104.
  14. “Some overdetermined boundary value problems with elliptical free boundaries”, en collaboration avec Gérard A. Philippin, in SIAM Journal of Mathematical Analysis, vol. 29, n.2, 1998, p. 309-320.
  15. “Existence results for some optimal partition problems”, en collaboration avec Dorin Bucur et Giuseppe Buttazzo, in Advances in Mathematical Sciences and Applications, vol. 8, n 2, 1998, p. 571-579.
  16. “Overdetermined problems on ring shaped domains”, en collaboration avec G.A. Philippin et H. Prébet, in Advances in Mathematical Sciences and Applications, vol. 9, n 2, 1999 p. 737-747.
  17. “Continuous Steiner Symmetrization and stability for the Dirichlet problem”, en collaboration avec Dorin Bucur, in Potential Analysis, vol. 13, 2000, p. 127-145.
  18. “Existence of a classical solution to a free boundary problem for the p-Laplace operator: (II) the interior convex case”, en collaboration avec Henrik Shahgholian, in Indiana Univ. Math. Journal, 49 (2000), no. 1, 311-323.
  19. “Some results about Schiffer’s conjectures”, en collaboration avec Thierry Chatelain, in Inverse Problems, vol. 15 (1999), p. 647-658.
  20. “Domain derivative of the leading eigenvalue of a model transport operator”, en collaboration avec Mourad Choulli et Mustapha Mokhtar-Kharroubi, in Transport theory and statistical physics, vol. 28 4 (1999), p. 403-418.
  21. “Existence of a classical solution to a free boundary problem for the p-Laplace operator I: the exterior convex case”, en collaboration avec Henrik Shahgholian, in Journal für die Reine und Angewandte Mathematik, Band 521 (2000), 85-97..
  22. “Minimization of the third eigenvalue of the Dirichlet Laplacian”, en collaboration avec Dorin Bucur, in Proceedings of the Royal Society of London, 456 (2000), 985-996.
  23. “Optimal location of the actuator for the pointwise stabilization of a string”, in C. R. Acad. Sci. Paris Sér. I Math, 330 (2000), no. 4, 275-280.
  24. “Optimization of the shape and the location of the actuators in an internal control problem”, en collaboration avec Hervé Maillot, in Bollettino della Unione Matematica Italiana, 4-B (2001), 737-757.
  25. “Continuity of the elasticity system solutions with respect to the geometrical domain variations”, en collaboration avec Dorin Bucur, Jan Sokolowski, A. Zochowski, in Advances in Mathematical Sciences and Applications, 11 (2001), no. 1, 57-73.
  26. “On the Bernoulli Free Boundary Problem and related Shape Optimization Problems”, en collaboration avec Mohammed Hayouni et Nadia
    Samouh, in Interfaces and free Boundaries, no 1, vol 3 (2001), 1-13.
  27. “A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative”, en collaboration avec Friedemann Brock, in Rendiconti del Circolo Matematico di Palermo, Serie II, Vol. 51 (2002), 375-390.
  28. “Le stade ne minimise pas $\lambda_2$ parmi les ouverts convexes du plan”, en collaboration avec Edouard Oudet, in C. R. Acad. Sci. Paris Sér. I Math, 332 (2001), 417-422.
  29. “Optimal pointwise stabilization of a string”, en collaboration avec Kais Ammari et Marius Tucsnak, in Asymptotic analysis, 28 (2001), 215-240.
  30. “On some recent advances in shape optimization”, en collaboration avec Gregoire Allaire, in C. R. Acad. Sci. Paris Sér. IIb Mech., 329 (2001), 383-396.
  31. “The one-phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition”, en collaboration avec Henrik Shahgholian, in Transactions of the AMS, 354 no. 6 (2002), 2399-2416.
  32. “An Optimum Design Problem in Magnetostatics”, en collaboration avec Gregory Villemin, in Modelisation Mathematique et Analyse Numerique, 36, no. 2 (2002), 223-239.
  33. “Optimal shape and position of the actuators for the stabilization of a string”, en collaboration avec Pascal Hebrard, in Systems and Control Letters, 48 (2003), 199-209.
  34. “On numerical solution of shape inverse problems”, en collaboration avec L. Jackowska-Strumillo, J. Sokolowski et A. Zochowski, in Computational Optimization and Applications, 23 (2002), 231-255.
  35. “Minimization problems for eigenvalues of the Laplacian”, PDF-FILE, in Journal of Evolution Equations, 3 (2003), 443-461.
  36. “Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions”, PDF-FILE, en collaboration avec Edouard Oudet, in Archive for Rational Mechanics and Analysis, 169 (2003), 73-87.
  37. “Approximate radial symmetry for solutions of a class of boundary value problems in ring-shaped domains”, en collaboration avec Gerard Philippin, in ZAMP, 54 (2003), 784-796.
  38. “Finite Dimensional Reduction for the Positivity of some Second Shape Derivatives”, en collaboration avec Michel Pierre et Mounir Rihani, in Methods and Applications of Analysis, 10, no 3 (2003), 457-476.
  39. “The multi-layer free boundary problem for the $p$-Laplacian in convex domains”, en collaboration avec Andrew Acker, Mikayel Poghosyan et Henrik Shahgholian, in Interfaces and free Boundaries,6 (2004), 81-103.
  40. “Positivity of the shape Hessian and instability of some equilibrium shapes”, en collaboration avec Michel Pierre et Mounir Rihani, in Mediterranean Journal of Mathematics, 1, (2004), 195-214.
  41. “On the first twisted Dirichlet eigenvalue”, PDF-FILE,
    en collaboration avec Pedro Freitas, in Communications in Analysis and Geometry, 12, no 5 (2004), 1083-1103.
  42. “A spillover phenomenon in the optimal location of actuators”, PDF-FILE, en collaboration avec Pascal Hébrard, in SIAM J. Control and Optimization, 44, no 1 (2005), 349-366.
  43. ” Mathematical challenges in shape optimizations”, PDF-FILE, en collaboration avec Jan Sokolowski, in Control and Cybernetics, 34, no 1 (2005), 37-57.
  44. ” Convergence results for a semilinear problem and for a Stokes problem in a periodic geometry”, PDF-FILE,
    en collaboration avec Séverine Baillet et Takéo Takahashi, in Asymptotic Analysis, 50, 3-4 (2006), 325-337.
  45. ” Shape minimization of dendritic attenuation”, PDF-FILE, en collaboration avec Yannick Privat, in Applied Mathematics and Optimization, 57, no 1 (2008), 1-17.
  46. ” Eliciting harmonics on strings”, PDF-FILE, en collaboration avec Steve Cox, in ESAIM COCV, 14,  (2008), 657-677.
  47. ” Some isoperimetric inequalities with application to the Stekloff problem”, PDF-FILE, en collaboration avec Gerard Philippin and Abdesselem Safoui, in Journal of Convex Analysis, 15, no3 (2008), 581-592.
  48. ” Une conduite cylindrique n’est pas optimale pour minimiser l’énergie dissipée par un fluide”, PDF-FILE, en collaboration avec Yannick Privat, in C. R. Acad. Sci. Paris Sér. I Math, 346, 19-20 (2008), 1057-1061.
  49. “Minimization of $\lambda_2(\Omega)$ with a perimeter constraint”, PDF-FILE, en collaboration avec Dorin Bucur et Giuseppe Buttazzo, in Indiana
    U. Math. Journal    , 58, no6 (2009), 2709-2728.
  50. ” What is the optimal shape of a pipe?”, PDF-FILE, en collaboration avec Yannick Privat, in Archive for Rational Mechanics and Analysis, 196, no1 (2010), 281-302.
  51. “On the maximization of a class of functionals on convex regions, and the characterization of the farthest convex set”, PDF-FILE, en collaboration avec Evans M. Harrell, in Mathematika, 56, Issue 02 (2010), 245 -265.
  52. “On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian”, PDF-FILE, en collaboration avec Pedro S. Antunes, in Proceedings of the Royal Society of London, Series A, 8 – 467 (2011), 1577-1603.
  53. “Optimal sets for a class of minimization problems with convex constraints”, PDF-FILE, en collaboration avec Chiara Bianchini, in Journal of Convex Analysis, vol. 19 no 2 (2012).
  54. `Rebuttal of Donnelly’s paper on the spectral gap”, PDF-FILE, in collaboration with Mark S. Ashbaugh and Richard S. Laugesen,  in Mathematische Zeitschrift, Volume 269, Issue 1 (2011), 5-7.
  55. “An isoperimetric inequality for a nonlinear eigenvalue problem”, PDF-FILE, en collaboration avec Gisella Croce et Giovanni Pisante, in Annales de l’IHP, Analyse non lineaire Volume 29, Issue 1 (2012), pp 21-34.
  56. “On some spectral problems arising in dynamic populations”, PDF-FILE, en collaboration avec El Haj Laamri et Didier Schmitt, in Communications in Pure and Applied Analysis,  Volume 11, Issue 6, 2012 Pages 2429-2443.
  57. “An optimal Poincar\’e-Wirtinger inequality in Gauss space”, PDF-FILE, en collaboration avec Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti, in Mathematical Research Letters, Volume 20 (2013) no 3, pp 449-457.
  58. “An overdetermined problem with non constant  boundary condition”, PDF-FILE en collaboration avec Chiara Bianchini et Paolo Salani, in Interfaces and Free Boundaries, volume 16 (2014), pp 215-241.
  59. “A new probabilistic canopy dynamics model (SLCD), suitable for evergreen and deciduous forest ecosystems”, in collaboration with Julien
    Sainte-Marie; Saint-Andre Laurent; Nouvellon Yann; Laclau Jean-Paul; Roupsard Olivier; Le Maire Guerric; NicolasDelpierre; Barrandon Matthieu,  in Ecological Modelling, volume 290 (2014), 121-133.
  60. “Real or Natural numbers interpretations and their effect on complexity”, in collaboration with Guillaume Bonfante and FlorianDeloup, in Theoretical Computer Science.
  61. “On the local minimizers of the Mahler volume”, PDF-FILE in collaboration with Evans Harrell and Jimmy Lamboley, in Journal of Convex Analysis, 22 (2015) 809–825.
  62. “Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift”, PDF-FILE  in collaboration with Barbara Brandolini; Francesco Chiacchio; Cristina Trombetti, in Journal of Differential Equations, Volume 259, Issue 2, 15 July 2015, Pages 708-727.
  63. “Elastic energy of a convex body “, PDF-FILE en collaboration avec Chiara Bianchini et Takéo Takahashi, in Mathematische Nachrichten 2016, Vol.289, Issue 5-6 (2016) , p. 546-574
  64. “On the minimization of total mean curvature”, PDF-FILE en collaboration avec Jeremy Dalphin, Simon Masnou et Takeo Takahashi,  in Journal of
    Geometric Analysis     vol. 26 (4) (2016), 2729-2750.
  65. “On the quantitative isoperimetric inequality in the plane”, en collaboration avec C. Bianchini et G. Croce, PDF-FILE in ESAIM COCV, vol. 23 no 2 (2017), 517–549
  66. “Elasticae and inradius”, en collaboration avec  Othmane Mounjid, in Archiv der Matematik, PDF-FILE vol. 108, issue 2  (February 2017), 181–196.
  67. “A new isoperimetric inequality for elasticae”, en collaboration avec D. Bucur Journal European Mathematical Society, PDF-FILE vol. {\bf 19} (2017), 3355–3376.
  68. “On two functionals involving the maximum of the torsion function”, en collaboration avec I. Lucardesi, G. Philippin,  in ESAIM COCV, PDF-FILE vol. 24 (2018) 1585-1604.
  69. “Optimal concavity of the torsion function”, en collaboration avec C. Nitsch, P. Salani, C. Trombetti, PDF-FILE in JOTA, vol. 178 issue 1 (2018), 26-35.
  70. “Minimization of the eigenvalues of the Dirichlet-Laplacian with a diameter constraint”, en collaboration avec B. Bogosel et I. Lucardesi, SIAM
    J. Mathematical Analysis    , PDF-FILE vol. 50 no 5, (2018), 5337-5361.
  71. “Optimizing the first Dirichlet eigenvalue of the Laplacian with an obstacle”, en collaboration avec D. Zucco, PDF-FILE  in Annali della Scuola Normale Superiore, vol. XIX (2019) 1535-1559.
  72. “Maximizing the second eigenvalue of the Neumann-Laplacian”, en collaboration avec D. Bucur, in Acta Mathematica, PDF-FILE  vol 222-2 (2019), 337-361.
  73. “Non-dispersal and density properties of infinite packings”, en collaboration avec A. Delyon et Y. Privat,  in SIAM J. Control and Optimization, PDF-FILE vol 57, Issue 2 (2019), 1467-1492.
  74. “Improved bounds for Hermite-Hadamard inequalities in higher dimensions”, en collaboration avec T. Beck, B. Brandolini, K. Burdzy, J. Langford, S. Larson, R. Smits, S. Steinerberger, in Journal of Geometric Analysis (2019) vol. 31, pp. 801-816  PDF-FILE
  75. “Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations”, en collaboration avec Idriss Mazari et Yannick Privat in ESAIM COCV vol. 27 no 56 PDF-FILE
  76. “Asymptotic behaviour of the Steklov problem on dumbbell domains”, en collaboration avec Dorin Bucur et Marco Michetti,  in Communications in PDE vol. 46 Issue 2, pp. 362-393 PDF-FILE.
  77. “The double queen Dido’s problem” en collaboration avec Lorenzo Cavallina et Shigeru Sakaguchi,  in The Journal of Geometric Analysis (2021), PDF-FILE.
  78. “From Steklov to Neumann via homogenisation” en collaboration avec Alexandre Girouard et Jean Lagac\’e, in Archive for Rational Mechanics and Analysis (2021) PDF-FILE.
  79. “Maximization of the Steklov eigenvalues with a diameter constraint”, en collaboration avec A. Al Sayed, B. Bogosel et F. Nacry, in SIAM J. Mathematical Analysis PDF-FILE
  80. “Hyperbolic solutions to Bernoulli ‘s free boundary problem”, en collaboration avec Michiaki Onodera, in Archive for Rational Mechanics and Analysis (2021) PDF-FILE
  81. “Body of constant width with minimal area in a given annulus”, en collaboration avec Ilaria Lucardesi, in Journal de l’Ecole Polytechnique, Tome 8 (2021) pp. 415-438 PDF-FILE