Articles

(2025), Exponential decay of the critical points in a discrete model of polyacetylene, Nonlinearity, vol. 38, n°1, p. 015002

(2024), A local surjection theorem with continuous inverse in Banach spaces, Rendiconti Lincei - Matematica E Applicationi, vol. 35, n°1, p. 1-15

(2024), Existence of minimizers for the Dirac-Fock Model of Crystals, Archive for Rational Mechanics and Analysis, vol. 248, n°63

(2023), A new definition of the Dirac-Fock ground state, Communications in Mathematical Physics, vol. 404, n°3, p. 1275-1307

(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

(2023), Phase transition in the Peierls model for polyacetylene, Annales Henri Poincaré

(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

(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

(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

(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

(2021), Multiple front standing waves in the FitzHugh-Nagumo equations, Journal of Differential Equations, vol. 302, p. 895-925

(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

(2021), Dirac-Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas, Annales Henri Lebesgue, vol. 4, p. 1421-1456

(2019), Domains for Dirac-Coulomb min-max levels, Revista Matematica Iberoamericana, vol. 35, n°3, p. 877-924

(2018), Derivation of the magnetic Euler-Heisenberg energy, Journal de mathématiques pures et appliquées, vol. 117, n°septembre 2018, p. 59-93

(2017), Smooth Solutions to Portfolio Liquidation Problems under Price-Sensitive Market Impact, Stochastic Processes and their Applications, vol. 128, n°3, p. 979-1006

(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

(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

(2011), Renormalization and asymptotic expansion of Dirac's polarized vacuum, Communications in Mathematical Physics, vol. 306, n°1, p. 1-33

(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

(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

(2009), Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms, Communications in Mathematical Physics, vol. 286, n°1, p. 179-215

(2008), Variational methods in relativistic quantum mechanics, Bulletin of the American Mathematical Society, vol. 45, n°4, p. 535–593

(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

(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

(2006), Normalized solutions to strongly indefinite semilinear equations, Advanced Nonlinear Studies, vol. 6, n°2, p. 323-347

(2006), The fixed energy problem for a class of nonconvex singular Hamiltonian systems, Journal of Differential Equations, vol. 230, n°1, p. 362-377

(2005), Some connections between Dirac-Fock and Electron-Positron Hartree-Fock, Annales Henri Poincaré, vol. 6, n°1, p. 85-102

(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

(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

(2005), Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation, Communications in Mathematical Physics, vol. 257, n°3, p. 515-562

(2003), Surface water waves as saddle points of the energy, Calculus of Variations and Partial Differential Equations, vol. 17, n°2, p. 199-220

(2003), A variational method for relativistic computations in atomic and molecular physics, International Journal of Quantum Chemistry, vol. 93, n°3, p. 149-155

(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

(2001), Nonrelativistic Limit of the Dirac-Fock Equations, Annales Henri Poincaré, vol. 2, n°5, p. 941-961

(2000), Variational characterization for eigenvalues of Dirac operators, Calculus of Variations and Partial Differential Equations, vol. 10, n°4, p. 321-347

(2000), On the Eigenvalues of Operators with Gaps. Application to Dirac Operators, Journal of Functional Analysis, vol. 174, n°1, p. 208-226

(2000), Minimization Methods for the One-Particle Dirac Equation, Physical Review Letters, vol. 85, n°19, p. 4020-4023

(1999), Solutions of the Dirac-Fock Equations for Atoms and Molecules, Communications in Mathematical Physics, vol. 203, n°3, p. 499-530

(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

(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

(1995), Stationary states of the nonlinear Dirac equation: A variational approach, Communications in Mathematical Physics, vol. 171, n°2, p. 323-350

(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

(1993), Looking for the Bernoulli shift, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 10, n°5, p. 561-590

(1992), Existence of infinitely many homoclinic orbits in Hamiltonian systems, Mathematische Zeitschrift, vol. 209, n°1, p. 27-42

(1990), A variational approach to homolinic orbits in Hamiltonian systems, Mathematische Annalen, vol. 288, n°1, p. 133-160

Chapitres d'ouvrage

(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

(2003), Computational approaches of relativistic models in quantum chemistry, in Le Bris, Claude, Handbook of Numerical Chemistry Elsevier, p. 899

(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

(2022), Dispersive Estimates for the Dirac–Coulomb Equation, in Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Qualitative Properties of Dispersive PDEs, Springer, 127-139 p.

(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.

(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.

(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.

(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.

(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

(2012), Two Hartree-Fock models for the vacuum polarization, Journées EDP 2012, Biarritz, France

Prépublications / Cahiers de recherche

(2023), A local surjection theorem with continuous inverse in Banach spaces, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 14 p.

(2023), Exponential decay of the critical points in a discrete model of polyacetylene, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 17 p.

(2018), A surjection theorem for singular perturbations with loss of derivatives, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 24 p.

(2014), An implicit function theorem for non-smooth maps between Fréchet spaces, Paris, Université Paris-Dauphine, 24 p.

(2012), Existence of kink solutions in a discrete model of the polyacetylene molecule, Paris, Université Paris-Dauphine, 20 p.