Homepage of Frédéric Hérau


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


  1. Coercivity, hypocoercivity, exponential time decay and simulations for discrete fokker-Planck equations, with G. Dujardin and P. Lafitte
    submitted 72 p. (January 2018). Pdf

  2. Cauchy theory and exponential stability for inhomogeneous boltzmann equation for hard potentials without cut-off, with D. Tonon and I. Tristani
    submitted 49 p. (October 2017). Pdf

  3. Short time diffusion properties of inhomogeneous kinetic equations with fractional collision kernel, with D. Tonon and I. Tristani
    submitted 34 p. (October 2017). Pdf

  4. Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff, with R. Alexandre and W.-X. Li
    submitted 68 p. (updated and enlarged version oct. 2017). Pdf

Publications and Works

  1. Holomorphic extensions of the De Gennes function, with V. Bonnaillie-Noël and N. Raymond
    to appear in Annales Mathématiques Blaise Pascal 10 p. (2017). Pdf

  2. Introduction to hypocoercive methods and applications for simple linear inhomogeneous kinetic models,
    Lectures on the Analysis of Nonlinear Partial Differential Equations Vol. 5, MLM5, 119–147 (2017). Pdf

  3. 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 15 p. (2017). Pdf

  4. 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

  5. Semiclassical tunneling and magnetic flux effects on the circle, with V. Bonnaillie-Noël and N. Raymond
    Journal of Spectral Theory EMS, 7 (3), pp.771-796 (2017). Pdf

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

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

  8. Artifical conditions for the linear elasticity equations, with V. Bonnaillie-Noël, M.Dambrine and G. Vial
    Math of Comp. 84 pp.1599-1632 (2015). Pdf

  9. 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

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

  11. 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

  12. 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 pp. 22-35 (2011). Pdf

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

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

  15. 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. 42 (2) pp.931-945. (2010). Pdf

  16. 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

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

  18. 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

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

  20. 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

  21. 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

  22. 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

  23. 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

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

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

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

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

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

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