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en libre service: (Unpublished texts with free access) [1] Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds, NotesSharpSP.pdf , 121 pages, 2002. Contains unpublished results.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 Unpublished results.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 Contains unpublished results.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] 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Existence, stability and instability for Einstein-scalar field Lichnerowicz equations, EinLich.pdf, Slides, Contains unpublished results, 46 pages, 2008/2009.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. 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. [9] Schrödinger-Proca constructions in the closed setting, SPConstructions, Slides from a talk, 44 pages, 2022. |
| Quelques articles
récents: (Some recent research papers) [1] Stationary Kirchhoff equations with powers, Advances in the Calculus of Variations, 11, 139-160, 2018. [2] 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. [3] 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. [4] 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. [5] 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. [6] Schrödinger-Poisson-Proca systems in EMS regime, Communications in Contemporary Mathematics, 24, 2150038, 2021. [7] Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case, Advances in Differential Equations, 27, 253-332, 2022. [8] A twist in sharp Sobolev inequalities with lower order remainder terms, Advances in the Calculus of Variations, 29 pages, à paraître. [9] Strong convergence in Bopp-Podolsky-Proca type constructions, Discrete and Continuous Dynamical Systems - Series A, 10 pages, à paraître. [10] Stability and critical dimension for Kirchhoff systems in closed manifolds, Preprint, 12 pages, 2023. |
Mise à jour: March 2023