Géométrie Riemannienne et analyse géométrique
Analyse non linéaire sur les
variétés
Equations aux dérivées partielles
Physique mathématique
Adresse:
Curriculum Vitae
A quoi servent les mathématiques | Monographies de
recherche: (Some research monographs) [1] Nonlinear analysis on manifolds: Sobolev spaces and inequalities, CIMS Lecture Notes, Courant Institute of Mathematical Sciences, New York University, Volume 5, 1999. Seconde édition publiée  conjointement avec l'American Mathematical Society, 290 pages, AMS/CIMS Lecture Notes , Volume 5, 2000. Version traduite en russe, Editions Tamara Rozhkovskaya, 2008. [2] The AB program in Geometric Analysis. Sharp Sobolev inequalities and related problems, Memoirs of the American Mathematical Society , avec O.Druet, 98 pages, MEMO/160/761, 2002. [3] Blow-up theory for elliptic PDEs in Riemannian geometry, Mathematical Notes , Princeton University Press, avec O.Druet et F.Robert, 218 pages, Volume 45, 2004. [4] Elliptic equations of Yamabe type, avec O.Druet, International Mathematics Research Surveys, IMRS, Issue 1, 1-113, 2005. [5] Compactness and stability for nonlinear elliptic equations, Zurich Lectures in Advanced Mathematics, ZLAM, 291 pages, European Mathematical Society, Volume 20, 2014. |
| Textes
en libre service: (Unpublished texts with free access) [1] Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds, NotesSharpSP.pdf , 121 pages, 2002. Contains unpublished results. [2] Variational methods and elliptic equations in Riemannian geometry, Notes from lectures given at ICTP,  NotesICTP.pdf , 63 pages, 2003. [3] Manifolds which are close to space forms and the Bemelmans, Min-Oo and Ruh smoothing effect of the Ricci flow, NotesSF.pdf , 5 pages, 2002. Unpublished results. [4] An introduction to fourth order nonlinear wave equations, avec B.Pausader, FourthOrderWaves.pdf , 48 pages, 2008. Contains unpublished results. [5] Super critical energy scale invariant equations in critical spaces, SuperCrit.pdf, 6 pages, 2010. Rewriting of a known result. [6] [New] A short (informal) introduction to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case, BPSPHebeySurvey.pdf, 20 pages, 2022. Transparents / Slides from various talks: [1] Existence, stability and instability for Einstein-scalar field Lichnerowicz equations, EinLich.pdf, Slides, Contains unpublished results, 46 pages, 2008/2009. [2] Elliptic stability for stationary Schrödinger equations,  Part I, PartII, and PartIII. Slides from a three parts course given in 2013. [3] Companion tables for the above slides on elliptic stability, Tables, 2013. [New] Updated version, March 2021, UpdatedVersion2021. [4] Elliptic stability for stationary Schrödinger equations, Part I, Part II, Part III, Part IV, Part V, Part VI. Slides (extended version) of a course given in 2015. [5] Klein-Gordon-Maxwell-Proca systems in closed manifolds, KGMPSlides, Slides from a talk, 37 pages, 2014. [6] Nonnegative solutions of stationary Kirchhoff systems, KirchhoffSyst, Slides from a talk, 30 pages, 2015. [7] Sationary Kirchhoff equations with powers, KPowersSlides, Slides from a talk, 32 pages, 2017. [8] Klein-Gordon-Maxwell-Proca systems in the Riemannian setting, KGMPSlides2, Slides from a talk, 39 pages, 2018. |
| Quelques articles
récents: (Some recent research papers) [1] Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal laplacian, avec O. Druet et J.Vétois, Journal of Functional Analysis, 258, 999–1059, 2010. [2] The Lin-Ni's conjecture for vector valued Schrödinger equations in the closed case, Communications in Pure and Applied Analysis, 9, 955–962, 2010. [3] Existence and a priori bounds for Klein-Gordon-Maxwell systems in fully inhomogeneous spaces, avec O. Druet, Communications in Contemporary Mathematics, 12, 831–869, 2010. [4] Asymptotic analysis for fourth order Paneitz equations with critical growth, avec F.Robert, Advances in the Calculus of Variations, 3, 229–276, 2011. [5] Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds, avec T.T.Truong, Journal für di reine und angewandte Mathematik (Crelle's journal), 667, 221-248, 2012. [6] Solitary waves in critical Abelian gauge theories, Discrete and Continuous Dynamical Systems - Series A, 32, 1747–1761, 2012. [7] Resonant states for the static Klein-Gordon-Maxwell-Proca system, avec J.Wei, Mathematical Research Letters, 19, 4, 953–967, 2012. [8] Schrödinger-Poisson systems in the 3-sphere, avec J.Wei, 33 pages, Calculus of Variations and Partial Differential Equations, 47, 25-54, 2013. [9] Stability of elliptic PDEs with respect to perturbations of the domain, avec O.Druet et P.Laurain, Journal of Differential Equations, 10, 3703–3718, 2013. [10] The Lichnerowicz equation in the closed case of the Einstein-Maxwell theory, avec G.Veronelli, Transactions of the American Mathematical Society, 366, 1179–1193, 2014. [11] Stationary Kirchhoff systems in closed 3-dimensional manifolds, avec P.D.Thizy, Calculus of Variations and Partial Differential Equations, 54, 2085-2114, 2015. [12] Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds. II, avec O.Druet et J.Vétois, Journal für di reine und angewandte Mathematik (Crelle's journal), 713, 149-179, 2016. [13] Stationary Kirchhoff systems in closed high dimensional manifolds, avec P.D.Thizy, Communications in Contemporary Mathematics, 18, Issue 02, 1550028 (53 pages), 2016. [14] Compactness and the Palais-Smale property for critical Kirchhoff equations in closed manifolds, Pacific Journal of Mathematics, 280, 41-50, 2016. [15] Multiplicity of solutions for critical Kirchhoff type equations, Communications in Partial Differential Equations, 41, 913-924, 2016. [16] Stationary Kirchhoff equations with powers, Advances in the Calculus of Variations, 11, 139-160, 2018. [17] Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case, avec P.D.Thizy, Journal of Partial Differential Equations, 31, 119-158, 2018. [18] Klein-Gordon-Maxwell-Proca type systems in the electro-magneto-static case: the high dimensional case, avec P.D.Thizy, Calculus of Variations and Partial Differential Equations, 58, 116 (31 pages), 2019. [19] Electro-Magnetic-Static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca Setting, Discrete and Continuous Dynamical Systems - Series A, 39, 6683-6712, 2019. [20] Strong convergence of the Bopp-Podolsky-Schrödinger-Proca system to the Schrödinger-Poisson-Proca system in the electro-magneto-static case, Calculus of Variations and Partial Differential Equations, 59, 198 (25 pages), 2020. [21] Schrödinger-Poisson-Proca systems in EMS regime, Communications in Contemporary Mathematics, doi 2150038 (6 pages), 2021. [22] Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case, Advances in Differential Equations, 80 pages, à paraître. |
Mise à jour: Avril 2022