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Research interests

Partial differential equations and Mathematical physics

Semiclassical analysis, pseudospectral estimates, spectrum, tunneling effect, Fokker-Planck operators, Witten Laplacian

Hypocoercivity, hypoellipticity, trend to the equilibrium for kinetic equations, linearized kinetic equations, Fokker-Planck, Vlasov-Poisson-Fokker-Planck, linear relaxation, Boltzmann, Landau, ...

transparent conditions, Dirichlet to Neumann operators, Ventcel's type conditions appearing in mechanics.

Semi-bounded pseudo-differential operators, Gaarding inequalities, Fefferman-Phong inequality, SAK principle, paradifferential operators


Publications and Works

  1. Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff, with R. Alexandred and W.-X. Li
    preprint 54 p. (2012). Pdf


  2. Artifcial conditions for the linear elasticity equations, with V. Bonnaillie-Noël, M.Dambrine and G. Vial
    preprint 32 p. (2012). Pdf


  3. Supersymmetric structures for second order differential operators, with J. Sjöstrand and M. Hitrik
    preprint 33 p. (2012). Pdf


  4. Global hypoelliptic estimates for Landau-type operators with external potential, with W.-X. Li
    to appear in Kyoto Journal of Mathematics 29 p. (2011). Pdf


  5. Tunnel effect and symmetries for Kramers Fokker-Planck type operators, with J. Sjöstrand and M. Hitrik
    Journal of the Inst. of Math. Jussieu 10(3) pp. 567--634 (2011). Pdf


  6. Multiscale expansion and numerical approximation for surface defects, with V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, S. Tordeux and G. Vial
    proceedings of CANUM 2010 14 p. (2010). Pdf


  7. Hypoelliptic estimates for some linear diffusive kinetic equations,
    Proceedings of the Journees EADP, Port d'albret 13 p. (2010). Pdf


  8. Anisotropic hypoelliptic estimates for Landau-type operators, with K. Pravda-Starov
    Journal de mathématiques pures et appliquées 95, pp. 513-552 (2011). Pdf


  9. On generalized Ventcel's type boundary conditions for Laplace operator in a bounded domain, with V. Bonnaillie-Noël, M.Dambrine and G. Vial
    SIAM J. Math. Anal. To appear (2010). Pdf


  10. Tunnel effect for the Kramers-Fokker-Planck type operators: return to equilibrium and applications, with J. Sjöstrand and M. Hitrik
    Int. Math. Res. Not. 2008, Article ID rnn057 48 p. (2008). Pdf


  11. Methodes microlocales pour les equations cinetiques,
    Habilitation a diriger des recherches, Reims 89 p. (2007). Pdf


  12. Tunnel effect for the Kramers-Fokker-Planck type operators, with J. Sjöstrand et M. Hitrik
    Ann. Henri Poincaré 9, 2 pp. 209--274 (2008). Pdf


  13. Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation,
    Asymptot. Anal. 46, 3-4 pp. 349--359 (2006). Pdf


  14. Short and long time behavior of the Fokker-Planck equation in a confining potential and applications,
    J. Funct. Anal., 244, 1 pp. 95--118 (2007). Pdf


  15. Semiclassical analysis for the Kramers-Fokker-Planck equation, with J.Sjostrand et C. Stolk
    Comm. Partial Differential Equations 30, 4-6 pp. 689--760 (2005). Pdf


  16. Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential, with F. Nier
    Arch. Rat. Mech. An. 171, 2 pp. 151-218 (2004). Pdf


  17. Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential (announced),
    Actes colloque Forges-les-Eaux 13 p. (2002). Pdf


  18. Melin inequality for paradifferential operators and applications,
    Comm. Partial Differential Equations 39, 7-8 pp. 1659-1680 (2002). Pdf


  19. Melin-Hörmander inequality in a Wiener type pseudo-differential algebra,
    Ark. För Mat. 39, 2 pp. 311-338 (2001). Pdf


  20. Fefferman's SAK principle in one dimension,
    Annales de l'Institut Fourier 50, 4 pp. 1229-1264 (2000). Pdf


  21. Fonction maximale associée à des symboles d'opérateurs pseudodifférentiels semi-bornés,
    C. R. Acad. Sci. 330, I pp. 449-454 (2000). Pdf


  22. Une inégalité de Gårding à bord,
    Proceedings of the EADP conference in La Chapelle sur Erdre Exp. 5 12 p., Nantes (2000). Pdf


  23. Opérateurs pseudo-différentiels semi-bornés,
    Thèse de l'Universite de Rennes 1 137 p. (1999). Pdf





Some slides

  1. Conditions au bord de type Ventcel généralisées pour l’opérateur de Laplace sur des domaines bornés.
    Slides of the talk given at ARAAM (Journée Amiéno-Rémoise), Reims 20 p. (apr. 2009). Pdf


  2. Tunnel effect for Kramers-Fokker-Planck operators.
    Slides of the talk given at imperial college, London 32 p. (feb 2009). Pdf