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Research interests


Partial differential equations and Mathematical physics

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

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


Prepublications


  1. Holomorphic extensions of the De Gennes function, with V. Bonnaillie-Noël and N. Raymond
    submitted 7 p. (December 2016). Pdf


  2. Curvature induced magnetic bound states: towards the tunneling effect for the ellipse, with V. Bonnaillie-Noël and N. Raymond
    Procedings of "journées EDP" at Roscoff 14 p. (November 2016). Pdf


  3. Introduction to hypocoercive methods and applications for simple linear inhomogeneous kinetic models,
    Course given at Morning side center of Mathematics 25 p. (November 2016). Pdf


  4. Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff, with R. Alexandre and W.-X. Li
    submitted 62 p. (updated and enlarged version dec. 2015). Pdf



Publications and Works


  1. On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential, with L. Thomann
    J. Funct. Anal 271, no.5 pp 1301-1340 (2016). Pdf


  2. Semiclassical tunneling and magnetic flux effects on the circle, with V. Bonnaillie-Noël and N. Raymond
    to appear in JST 20 p. (revised version 2015). Pdf


  3. Magnetic WKB constructions, with V. Bonnaillie-Noël and N. Raymond
    Arch. Ration. Mech. Anal. 221, no.2 817–891 (2016). Pdf


  4. Tunnel effect for semiclassical random walk, with J.-F. Bony and L. Michel
    Anal. PDE 8, no. 2 pp 289–332 (2015). Pdf


  5. Artifcial conditions for the linear elasticity equations, with V. Bonnaillie-Noël, M.Dambrine and G. Vial
    Math of Comp. 32 p. (2014). Pdf


  6. Global hypoelliptic estimates for Landau-type operators with external potential, with W.-X. Li
    Kyoto J. Math. 53, no. 3 pp. 533–565. (2013). Pdf


  7. Supersymmetric structures for second order differential operators, with J. Sjöstrand and M. Hitrik
    Algebra i analiz vol25 n2 pp 125-154 (2013). Pdf


  8. 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


  9. 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


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


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


  12. 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


  13. 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


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


  15. 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


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


  17. 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


  18. 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


  19. 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


  20. 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


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


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


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


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


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


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