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Marc Briane

Professeur des Universités
 
INSA de Rennes

20 avenue des Buttes de Coësmes - CS 70839
35708 Rennes Cedex 7 FRANCE

Tél : 33 (0)2 23 23 85 39
    33 (0)2 23 23 84 90
    Marc.Briane@insa-rennes.fr
Affectations :

Topics of research:

Publications:

  1. Three models of non-periodic fibrous materials obtained by homogenization, M2AN, Mod. Math. Ana. Num., 27(6) (1993), 759-775.

  2. Homogenization of a non-periodic material, J. Math. Pures Appl.,73 (1994), 47-66.

  3. Corrector for the homogenization of a laminate, Advances Mat. Sci. Appl., 4 (2) (1994), 357-379.

  4. H-convergence for perforated domains, with A. Damlamian & P. Donato, in Nonlinear Par. Dif. Equ. & App., Collège de France Seminar XIII, D. Cioranescu & J.L. Lions eds., Pitman Res. Notes in Math. Ser., Longman, New York, 391 (1998), 62-100.

  5. Multiscale convergence and reiterated homogenisation, with G. Allaire, Proc. Royal Soc. Edin., 126A (1996), 297-342.

  6. Homogenization of some weakly connected materials, Ricerche di Matematica, 47 (1) (1998), 51-94.

  7. Homogenization of perforated laminates, Applicable Analysis, 67 (1997), 21-57.

  8. The Poincaré-Wirtinger inequality for the homogenization in perforated domains, Boll. Uni. Mate. Ital., 11-B (7) (1997), 53-82.

  9. Homogenization of the torsion problem and the Neumann problem in non-regular periodically perforated domains, M3AS, 7 (6) (1997), 847-870.

  10. Homogenization of two randomly weakly connected materials, with L. Mazliak, Portugaliae Mathematica,55 (2) (1998), 187-207.

  11. Convergence of the spectrum of a weakly connected domain, Ann. Mate. Pura Appl., 177 (4) (1999), 1-35.

  12. Optimal conditions of convergence and effects of anisotropy in the homogenization of non-uniformly elliptic problems, Asymptotic Analysis, 25 (2001), 271-297.

  13. Increase of dimension by homogenization, Potential Analysis, 14 (3) (2001), 233-268.

  14. Homogenization of a class of non-uniformly elliptic monotone operators, Nonlinear Analysis T.M.A., 48 (2002), 137-158.  

  15. Non-Markovian quadratic forms obtained by homogenization, Boll. Uni. Mate. Ital. 6-B (8) (2003), 323-337.

  16. Homogenization of non-uniformly bounded operators, Arch. Rat. Mech. Ana., 164 (2002), 73-101.

  17. Fibered microstructures for some nonlocal Dirichlet forms,, with N. Tchou, Ann. Scu. Norm. Sup. Pisa Cl. Sci, 30 (4) (2001), 681-711.

  18. Homogenization in general periodically perforated domains by a spectral approach, Calc. Var. Part. Diff. Equa., 15 (2002), 1-24.

  19. Boundary effects in fibered reinforced media, with N. Tchou, C.R.A.S. Paris, 333 Série I (2001), 173-177.

  20. A new approach for the homogenization of high-conductivity periodic problems. Application to a general distribution of one directional fibers, SIAM J. Math. Anal., 35 (1) (2003), 33-60.

  21. Is it wise to keep laminating ?, with V. Nesi, ESAIM: Con. Opt. Cal. Var., 10 (2004), 452-477.

  22. Homogenization of the Stokes equations with high-contrast viscosity, J. Math. Pures Appl., 82 (7) (2003), 843-876.

  23. Change of sign of the corrector's determinant for homogenization in three-dimensional conductivity, with G.W. Milton & V. Nesi, Arch. Rat. Mech. Anal., 173 (1) (2004), 133-150.

  24. Variations on a strange semi-continuity result, with F. Murat & G. Mokobodzki, J. Func. Anal., 227 (1) (2005), 78-112.

  25. Lack of compactness in the two-scale convergence, with J. Casado-Díaz, SIAM J. Math. Anal., 37 (2) (2005), 333-346.

  26. Nonlocal effects in two-dimensional conductivity, Arch. Rat. Mech. Anal., 182 (2) (2006), 255-267.

  27. Homogenization of nonlinear variationals problems with low-conductivity thin regions, with A. Braides, Appl. Math. Opt., 55 (1) (2007), 1-29.

  28. Expansion formulas of the homogenized determinant for anisotropic checkerboards, with Y. Capdeboscq, Proc. Royal Soc. London A, 462 (2073) (2006), 2759-2779.

  29. On cloaking for elasticity and physical equations with a transformation invariant form", with G.W. Milton & J.R. Willis, New J. Physics, 8 (2006), 248.

  30. Two-dimensional div-curl results. Application to the lack of nonlocal effects in homogenization, with J. Casado-Díaz, Com. Part. Diff. Equa., 32 (2007), 935-969.

  31. Asymptotic behaviour of equicoercive diffusion energies in two dimension, with J. Casado-Díaz, Calc. Var. Part. Diff. Equa., 29 (4) (2007), 455-479.

  32. Distributional convergence of null Lagrangians under very mild conditions, with V. Nesi, Dis. Cont. Dyn. Syst. B, 8 (2) (2007), 493-510.

  33. Homogenization of two-dimensional elasticity problems with very stiff coefficients, with M. Camar-Eddine, J. Math. Pures Appl., 88 (2007), 483-505.

  34. Semi-strong convergence of sequences satisfying a variational inequality, with F. Murat & G. Mokobodzki, Annales IHP, Ana. Non Lin., 25 (1) (2008), 121-133.

  35. Homogenization of the two-dimensional Hall effect, with D. Manceau & G.W. Milton, J. Math. Ana. App., 339 (2008), 1468-1484.

  36. Duality results in the homogenization of two-dimensional high-contrast conductivities, with D. Manceau, Networks and Heterogeneous Media, 3 (3) (2008), 509-522.

  37. Compactness of sequences of two-dimensional energies with a zero-order term. Application to three-dimensional nonlocal effects, with J. Casado-Díaz, Calc. Var. Part. Diff. Equa., 33 (2008), 463-492.

  38. Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients, with J. Casado-Díaz, J. Diff. Equa., 245 (2008), 2038-2054.

  39. Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient, with G.W. Milton, Arch. Rat. Mech. Anal., 193 (3) (2009), 715-736.

  40. The div-curl lemma "trente ans après": an extension and an application to the G-convergence of unbounded monotone operators, with J. Casado-Díaz & F. Murat, J. Math. Pures Appl., 91 (2009), 476-494.

  41. Giant Hall effect in composites, with G.W. Milton, Multiscale Model. Simul., 7 (3) (2009), 1405-1427.

  42. Homogenization of non-uniformly bounded periodic diffusion energies in dimension two, with A. Braides & J. Casado-Díaz, Nonlinearity, 22 (2009), 1459-1480.

  43. An antisymmetric effective Hall matrix, with G.W. Milton, SIAM J. Appl. Math., 70 (6) (2010), 1810-1820.

  44. Homogenization of the magneto-resistance in dimension two, M3AS, Math. Mod. Met. Appl. Sci., 20 (7) (2010), 1161-1177.

  45. New bounds on strong field magneto-transport in multiphase columnar composites, with G.W. Milton, SIAM J. Appl. Math., 70 (8) (2010), 3272-3286.

  46. Estimate of the pressure when its gradient is the divergence of a measure. Applications., with J. Casado-Díaz , ESAIM COCV, 17 (2011), 1066–1087.

  47. Bounds on strong field magneto-transport in three-dimensional composites, with G.W. Milton, J. Math. Phys., 52 103705 (2011), pp. 18.

  48. A drift homogenization problem revisited, with P. Gérard, Ann. Scu. Norm. Sup. Pisa Cl. Sci, 11 (5) (2012), 1-39.

  49. An optimal condition of compactness for elasticity problems involving one directional reinforcement, with M. Camar-Eddine, J. Elasticity, 107 (2012), 11-38.

  50. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three, with L. Pater, J. Math. Anal. Appl. 393 (2) (2012), 563-589.

  51. Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations, with J. Casado-Díaz, Arch. Rat. Mech. Anal., 205 (3) (2012), 753-794.

  52. Homogenization with an oscillating drift: from L^2-bounded to unbounded drifts, 2d compactness results and 3d nonlocal effects, Ann. Mate. Pura Appl., 192 (5) (2013), 853-878.

  53. Interior regularity estimates in high conductivity homogenization and application, with Y. Capdeboscq & L. Nguyen, Arch. Rat. Mech. Anal., 207 (1) (2013), 75-137.

  54. Homogenization of convex functionals which are weakly coercive and not equibounded from above, with J. Casado-Díaz, Ann. I.H.P. (C) Non Lin. Anal., 30 (4) (2013), 547-571.

  55. Which electric fields are realizable in conducting materials?, with G.W. Milton & A. Treibergs, ESAIM: Math. Model. Numer. Anal., 48 (2) (2014), 307-323.

  56. Magneto-resistance in three-dimensional composites, with L. Pater, Asymptotic Analysis, 86 (2014), 165-197.

  57. Isotropic realizability of electric fields around critical points, Disc. Cont. Dyn. Syst. B, 19 (2) (2014), 353-372.

  58. First Bloch eigenvalue in high contrast media, with M. Vanninathan, J. Math. Physics, 55, 011501 (2014), pp. 15.

  59. Homogenization of systems with equi-integrable coefficients, with J. Casado-Díaz, ESAIM COCV, 20 (04) (2014), 1214-1223.

  60. Loss of ellipticity through homogenization in linear elasticity, with G. Francfort, M3AS, Math. Mod. Met. Appl. Sci., 25 (5) (2015), 905-928.

  61. Isotropic realizability of current fields in R^3, with G.W. Milton, SIAM J. App. Dyn. Sys., 14 (2) (2015), 1165-1188.

  62. A class of second-order linear elliptic equations with drift: renormalized solutions, uniqueness and homogenization, with J. Casado-Díaz, Potential Analysis, 43 (3) (2015), 399-413.

  63. A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian, with J. Casado-Díaz, J. Diff. Equa., 260 (7) (2016), 5678-5725.

  64. Isotropic realizability of a strain field for the two-dimensional incompressible elasticity system, Inverse Problems, 32 (6) (2016), 065002, 22 pp.

  65. A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures, with G. Allaire & M. Vanninathan, accepted and to appear in SeMA Journal.