CEREMADE
Séré Éric
Full Professor
Publications
Articles
Catto I., Meng L., Paturel E., Séré É. (2024), Existence of minimizers for the Dirac-Fock Model of Crystals, Archive for Rational Mechanics and Analysis, vol. 248, n°63 
Dolbeault J., Esteban M., Séré É. (2023), Corrigendum to: “On the eigenvalues of operators with gaps. Application to Dirac operators” [J. Funct. Anal. 174 (1) (2000) 208–226], Journal of Functional Analysis, vol. 284, n°1
Cacciafesta F., Séré É., Zhang J. (2023), Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications, Communications in Partial Differential Equations, vol. 48, n°3, p. 355-385
Dolbeault J., Esteban M., Séré É. (2023), Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators, Journal of Spectral Theory, vol. 13, n°2, p. 491–524
Gontier D., Kouande A., Séré É. (2023), Phase transition in the Peierls model for polyacetylene, Annales Henri Poincaré
Séré É. (2023), A new definition of the Dirac-Fock ground state, Communications in Mathematical Physics, vol. 404, n°3, p. 1275-1307
Ekeland I., Séré É. (2021), A surjection theorem for maps with singular perturbation and loss of derivatives, Journal of the European Mathematical Society, vol. 23, n°10, p. 323–3349
Esteban M., Lewin M., Séré É. (2021), Dirac-Coulomb operators with general charge distribution. II. The lowest eigenvalue, Proceedings of the London Mathematical Society, vol. 123, n°4, p. 345-383
Chen C-N., Séré É. (2021), Multiple front standing waves in the FitzHugh-Nagumo equations, Journal of Differential Equations, vol. 302, p. 895-925
Chupin M., Dupuy M-S., Legendre G., Séré É. (2021), Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, n°6, p. 2785 - 2825
Esteban M., Lewin M., Séré É. (2021), Dirac-Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas, Annales Henri Lebesgue, vol. 4, p. 1421-1456
Esteban M., Lewin M., Séré É. (2019), Domains for Dirac-Coulomb min-max levels, Revista Matematica Iberoamericana, vol. 35, n°3, p. 877-924
Gravejat P., Lewin M., Séré É. (2018), Derivation of the magnetic Euler-Heisenberg energy, Journal de mathématiques pures et appliquées, vol. 117, n°septembre 2018, p. 59-93
Graewe P., Horst U., Séré É. (2017), Smooth Solutions to Portfolio Liquidation Problems under Price-Sensitive Market Impact, Stochastic Processes and their Applications, vol. 128, n°3, p. 979-1006
Cacciafesta F., Séré É. (2016), Local smoothing estimates for the massless Dirac-Coulomb equation in 2 and 3 dimensions, Journal of Functional Analysis, vol. 271, n°8, p. 2339-2358
Gravejat P., Lewin M., Hainzl C., Séré E. (2013), Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields, Archive for Rational Mechanics and Analysis, vol. 208, n°2, p. 603-655
Gravejat P., Lewin M., Séré E. (2011), Renormalization and asymptotic expansion of Dirac's polarized vacuum, Communications in Mathematical Physics, vol. 306, n°1, p. 1-33
Gravejat P., Séré E., Lewin M. (2009), Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms, Communications in Mathematical Physics, vol. 286, n°1, p. 179-215
Lewin M., Séré E., Hainzl C. (2009), Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics, Archive for Rational Mechanics and Analysis, vol. 192, n°3, p. 453-499
Lewin M., Séré E. (2009), Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schrödinger Operators), Proceedings of the London Mathematical Society, vol. 100, n°3, p. 864-900
Séré E., Lewin M., Esteban M. (2008), Variational methods in relativistic quantum mechanics, Bulletin of the American Mathematical Society, vol. 45, n°4, p. 535–593
Hainzl C., Solovej J., Séré E., Lewin M. (2007), A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics, Physical Review. A, Atomic, Molecular and Optical Physics and Quantum Information, vol. 76, n°5, p. 52-104
Séré E., Carminati C., Tanaka K. (2006), The fixed energy problem for a class of nonconvex singular Hamiltonian systems, Journal of Differential Equations, vol. 230, n°1, p. 362-377
Esteban M., Séré E., Buffoni B. (2006), Normalized solutions to strongly indefinite semilinear equations, Advanced Nonlinear Studies, vol. 6, n°2, p. 323-347
Séré E., Dolbeault J., Esteban M. (2006), General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators., Journal of the European Mathematical Society, vol. 8, n°2, p. 243-251
Hainzl C., Séré E., Lewin M. (2005), Self-consistent solution for the polarized vacuum in a no-photon QED model, Journal of Physics A: Mathematical and Theoretical, vol. 38, n°20, p. 4483-4499
Hainzl C., Séré E., Lewin M. (2005), Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation, Communications in Mathematical Physics, vol. 257, n°3, p. 515-562
Toland J., Séré E., Buffoni B. (2005), Minimisation methods for quasi-linear problems, with an application to periodic water waves, SIAM Journal on Mathematical Analysis, vol. 36, n°4, p. 1080-1094
Séré E., Esteban M., Barbaroux J-M. (2005), Some connections between Dirac-Fock and Electron-Positron Hartree-Fock, Annales Henri Poincaré, vol. 6, n°1, p. 85-102
Dolbeault J., Séré E., Esteban M. (2003), A variational method for relativistic computations in atomic and molecular physics, International Journal of Quantum Chemistry, vol. 93, n°3, p. 149-155
Toland J., Séré E., Buffoni B. (2003), Surface water waves as saddle points of the energy, Calculus of Variations and Partial Differential Equations, vol. 17, n°2, p. 199-220
Séré E., Dolbeault J., Esteban M. (2002), About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators, Séminaire Équations aux dérivées partielles (dit "Goulaouic-Schwartz"), p. Exposé n°XVIII
Séré E., Esteban M. (2001), Nonrelativistic Limit of the Dirac-Fock Equations, Annales Henri Poincaré, vol. 2, n°5, p. 941-961
Séré E., Vanbreugel M., Dolbeault J., Esteban M. (2000), Minimization Methods for the One-Particle Dirac Equation, Physical Review Letters, vol. 85, n°19, p. 4020-4023
Séré E., Esteban M., Dolbeault J. (2000), Variational characterization for eigenvalues of Dirac operators, Calculus of Variations and Partial Differential Equations, vol. 10, n°4, p. 321-347
Séré E., Esteban M., Dolbeault J. (2000), On the Eigenvalues of Operators with Gaps. Application to Dirac Operators, Journal of Functional Analysis, vol. 174, n°1, p. 208-226
Séré E., Esteban M. (1999), Solutions of the Dirac-Fock Equations for Atoms and Molecules, Communications in Mathematical Physics, vol. 203, n°3, p. 499-530
Esteban M., Séré E., Georgiev V. (1996), Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations, Calculus of Variations and Partial Differential Equations, vol. 4, n°3, p. 265-281
Georgiev V., Esteban M., Séré E. (1996), Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems, Letters in Mathematical Physics, vol. 38, n°2, p. 217-220
Séré E., Esteban M. (1995), Stationary states of the nonlinear Dirac equation: A variational approach, Communications in Mathematical Physics, vol. 171, n°2, p. 323-350
Séré E. (1995), Homoclinic orbits on compact hypersurfaces in 293-1293-1293-1, of restricted contact type, Communications in Mathematical Physics, vol. 172, n°2, p. 293-316
Séré É. (1993), Looking for the Bernoulli shift, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 10, n°5, p. 561-590
Séré E. (1992), Existence of infinitely many homoclinic orbits in Hamiltonian systems, Mathematische Zeitschrift, vol. 209, n°1, p. 27-42
Zelati V., Ekeland I., Séré E. (1990), A variational approach to homolinic orbits in Hamiltonian systems, Mathematische Annalen, vol. 288, n°1, p. 133-160
Chapitres d'ouvrage
Esteban M., Lewin M., Séré É. (2023), Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics, in Jean-Michel Morel, Bernard Teissier, Mathematics Going Forward Springer, p. 487–497
Indelicato P., Dolbeault J., Séré E., Esteban M., Desclaux J. (2003), Computational approaches of relativistic models in quantum chemistry, in Le Bris, Claude, Handbook of Numerical Chemistry Elsevier, p. 899
Séré E., Esteban M. (1997), Existence and multiplicity of solutions for linear and nonlinear Dirac problems, in Sulem, Catherine, Partial differential equations and their applications, Providence (RI): American Mathematical Society, p. 315
Communications avec actes
Cacciafesta F., Séré É., Zhang J. (2022), Dispersive Estimates for the Dirac–Coulomb Equation, in Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Qualitative Properties of Dispersive PDEs, Springer, 127-139 p.
Gravejat P., Hainzl C., Lewin M., Séré E. (2016), Deux modèles effectifs pour les champs électromagnétiques dans le vide de Dirac, in François Golse et Frank Merle, Séminaire Laurent Schwartz — EDP et applications (2015-2016), Séminaire Laurent Schwartz -EDP et applications, Ex No. 14, 20 p.
Esteban M., Séré E. (2006), Dirac-Fock models for atoms and molecules and related topics, in Zambrini, Jean-Claude, XIVth International Congress on Mathematical Physics: Lisbon 28 July - 2 August 2003, Lisbon, World Scientific, 21-28 p.
Esteban M., Séré É. (2002), A max-min principle for the ground state of the Dirac-Fock functional, in , Taxco, IEEE - Institute of Electrical and Electronics Engineers, 135-141 p.
Séré E., Esteban M. (2002), A max-min principle for the ground state of the Dirac-Fock functional, in Weder, Ricardo, Mathematical results in quantum mechanics : a conference on QMATH-8, mathematical results in quantum mechanics, Universidad Nacional Autonoma de México, Taxco, México, December 10-14, 2001, Taxco, American Mathematical Society, 350 p.
Dolbeault J., Esteban M., Séré E. (2000), Variational Methods in Relativistic Quantum Mechanics: New Approach to the Computation of Dirac Eigenvalues, in Le Bris, Claude, Mathematical models and methods for ab initio quantum chemistry, Edimbourg, Springer, 246 p.
Communications sans actes
Séré E., Gravejat P., Lewin M., Hainzl C. (2012), Two Hartree-Fock models for the vacuum polarization, Journées EDP 2012, Biarritz, France
Prépublications / Cahiers de recherche
Gontier D., Kouande A., Séré É. (2023), Exponential decay of the critical points in a discrete model of polyacetylene, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 17 p.
Ekeland I., Séré É. (2023), A local surjection theorem with continuous inverse in Banach spaces, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 14 p.
Séré E., Ekeland I. (2014), An implicit function theorem for non-smooth maps between Fréchet spaces, Paris, Université Paris-Dauphine, 24 p.
Séré E., Arroyo M. (2012), Existence of kink solutions in a discrete model of the polyacetylene molecule, Paris, Université Paris-Dauphine, 20 p.