ROBERT Frédéric

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Vita in English or in French.

Education:

1992: Distinction at the « Concours Général » in Physics.
1994: « École Normale Supérieure de Cachan », Cachan, France.
1997: « Agrégation » of Mathematics. Rank: 15.
1998: Phd studies. Thesis advisor: Emmanuel Hebey. Thesis defended on November 26th, 2001.
2007: Habilitation to conduct researches. Defended on June 28th, 2007. Download .pdf file (in French).

Bibliographic references

• MathSciNet
• ZentraBlatt
• Google Scholar
• ArXiv.org
• HAL

Some mathematical texts

A. Fourth order equations with critical growth in Riemannian geometry. Notes from lectures given at Madison and Berlin (not submitted). Download .pdf
B. Existence et asymptotiques optimales des fonctions de Green des opérateurs elliptiques
d’ordre deux. (Existence and optimal asymptotics for the Green’s function of second order elliptic operators). Personal notes in French (not submitted). Download .pdf
C. Construction and asymptotics for the Green’s function with Neumann boundary condition. Personal notes (not submitted). Download .pdf.
D. Struwe’s compactness for free functionals involving the bi-harmonic operator. Personal notes (not submitted). Download .pdf.
E. Extremals for Hardy-Sobolev type inequalities: the influence of the curvature. . Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imaging, 1-15, Sémin. Congr., 22, Soc. Math. France, Paris, 2011. Download .pdf.
F. On the equivalence of the Kazdan-Warner and the Pohozaev identities, with Olivier Druet. Personal notes (not submitted). Download .pdf.
G. Extremals for the Hardy-Sobolev inequalities on cones, avec Nassif Ghoussoub. Informal note extracted from reference [36]. Download .pdf.
H. Green’s function for a singular Hardy-type operator with boundary singularity. Informal note. Download .pdf.

Main publications:

1. Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent. The radial case, Advances in Differential Equations, 6, (2001), 821-846. Download .pdf.
2. Asymptotic profile for the sub-extremals of the sharp Sobolev inequality on the sphere, with Olivier Druet, Communications in Partial Differential Equations, 26, (2001), 743-778. Download .pdf.
3. Coercivity and Struwe’s compactness for Paneitz type operators with constant coefficients, with Emmanuel Hebey, Calculus of Variations and Partial Differential equations, 13, (2001), 491-517. Download .pdf.
4. Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: The radial case II. Nonlinear Differential Equations and Applications, 9, (2002), 361-384. Download .pdf.
5. Positive solutions for a fourth order equation invariant under isometries,Proceedings of the AMS, 131, (2003), 1423-1431. Download .pdf.
6. Mountain-Pass critical points for Paneitz-Branson operators, with Pierpaolo Esposito, Calculus of Variations and Partial Differential Equations, 15, (2002), 493-517. Download .pdf.
7. Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case, with Veronica Felli and Emmanuel Hebey, Nonlinear Differential Equations and Applications, 12, (2005), 171-213. Download .pdf.
8. Blow-up theory for elliptic PDEs in Riemannian geometry, with Olivier Druet and Emmanuel Hebey Mathematical Notes, Princeton University Press, Volume 45. Result announced in Electronic Research Announcements of the AMS, 9, (2003), 19-25.
9. Sharp solvability conditions for a fourth order equation with perturbation, with Kunnath Sandeep, Differential and Integral Equations, 16, (2003), 1181-1214. Download .pdf.
10. Asymptotic profile for a fourth order pde with critical exponential growth in dimension four, with Michael Struwe. Advanced Nonlinear Studies, 4, (2004), 397-415. Download .pdf.
11. Compactness and global estimates for the geometric Paneitz equation in high dimensions, with Emmanuel Hebey. Electronic Research Announcements of the AMS, 10, (2004), 135-141. Download .pdf.
12. Critical functions and optimal Sobolev inequalities, Mathematische Zeischrift, 249, (2005), 485-492. Download .pdf.
13. Compactness and global estimates for a fourth order equation of critical Sobolev growth arising from conformal geometry, with Emmanuel Hebey and Yuliang Wen. Communications in Contemporary Mathematics, 8, (2006), 9-65. Download .pdf.
14. The effect of curvature on the best constant in Hardy-Sobolev inequalities, with Nassif Ghoussoub. Geometric And Functional Analysis (GAFA), 16, (2006), 1201-1245. Download .pdf.
15. Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth, with Olivier Druet. Proceedings of the AMS, 134, (2006), 897-908. Download .pdf.
16. Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth, with Nassif Ghoussoub. International Mathematics Research Papers (IMRP), Volume 2006, Article ID 21867, 1-85. Download .pdf.
17. Concentration phenomena for Liouville’s equation in dimension four, with Adimurthi and Michael Struwe. Journal of the European Mathematical Society, 8, (2006), 171-180. Download .pdf.
18. Concentration phenomena for a fourth order equation with exponential growth: the radial case. Journal of Differential Equations, 231, (2006), 135-164. Download .pdf.
19. Quantization effects for a fourth order equation of exponential growth in dimension four. The Royal Society of Edinburgh Proceedings A, 137A, (2007), 531-553. Download .pdf.
20. On the local Nirenberg problem for the Q-curvatures with Philippe Delanoe. Pacific Journal of Mathematics, 231, (2007), 293-304. Download .pdf.
21. On the influence of the Kernel of the bi-harmonic operator on fourth order equations with exponential growth. Sixth international conference on « Dynamical Systems and Differential Equations », Poitiers, June 2006. Discrete and continuous dynamical systems, Supplement 2007, 875-882. Download .pdf.
22. Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition, with Juncheng Wei. Indiana University Mathematics Journal, 57, (2008), 2039-2060. Download .pdf.
23. Elliptic equations with critical growth and a large set of boundary singularities, with Nassif Ghoussoub. Transactions of the AMS, 361 (2009), no. 9, 4843-4870. Download .pdf.
24. On a p-Laplace equation with multiple critical nonlinearities, with Roberta Filippucci et Patrizia Pucci. Journal des Mathématiques Pures et Appliquées, 91, (2009), 156-177. Download .pdf.
25. Positivity and almost positivity of biharmonic Green’s functions under Dirichlet boundary conditions, with Hans-Christoph Grunau. Archive for Rational Mechanics and Analysis, 195, (2010) 865-898. Download .pdf.
26. The heat flow with a critical exponential nonlinearity, with Tobias Lamm et Michael Struwe. Journal of Functional Analysis, 257, (2009), 2951-2998. Download .pdf.
27. Admissible $Q-$curvatures under isometries for the conformal GJMS operators. Nonlinear elliptic partial differential equations, 241-259, Contemporary Mathematics, 540, Amer. Math. Soc., Providence, RI, 2011. Volume in the honor of Jean-Pierre Gossez. Download .pdf.
28. The Lin-Ni’s conjecture for mean convex domains . with Olivier Druet and Juncheng Wei. Memoirs of the AMS, 218, (2012), 105pp. Download .pdf.
29. Asymptotic analysis for fourth order Paneitz equations with critical growth . with Emmanuel Hebey. Advances in the Calculus of Variations, 4, (2011), 229-275. Download .pdf.
30. Optimal estimates from below for biharmonic Green functions . with Hans.-Christoph Grunau and Guido Sweers. Proceedings of the AMS, 139, (2011), 2151-2161. Download .pdf .
31. Sign-changing blow-up for scalar curvature type equations . with Jerome Vetois. Communications in Partial Differential Equations, Volume 38, Issue 8, August 2013, pages 1437-1465. Download .pdf.
32. Uniform estimates for polyharmonic Green functions in domains with small holes. with Hans-Christoph Grunau. Contemporary Mathematics, 595, (2013), 263-272. Download .pdf.
33. A general theorem for the construction of blowing-up solutions to some elliptic nonlinear equations via Lyapunov-Schmidt’s finite-dimensional reduction. with Jerome Vetois. Concentration Compactness and Profile Decomposition, (TIFR CAM, Bangalore, 2011), Trends in Mathematics, 95-116, Springer. Download .pdf.
34. Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non locally conformally flat manifolds.
with Jerome Vetois. Journal of Differential Geometry,, 98, (2014), 349-356. Download .pdf.
35. Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold.
with Jerome Vetois. Calculus of Variations and PDEs, 54, (2015), 693-716. DOI10.1007/s00526-014-0802-1 . Download .pdf.
36. On the Hardy-Schrodinger operator with a boundary singularity . with Nassif Ghoussoub. Analysis and PDEs, 10-5, (2017), 1017-1079. DOI 10.2140/apde.2017.10.1017. Download .pdf.
37. Sobolev inequalities for the Hardy-Schrodinger operator: Extremals and critical dimensions, with Nassif Ghoussoub. Bulletin of Mathematical Sciences, 6, (2016), no. 1, 89-144. DOI: 10.1007/s13373-015-0075-9. Download .pdf.
38. Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign-changing nonlinearity .
with Florica Cirstea. Proceedings of the London Mathematical Society, (3), 114, (2017), 1-34. DOI: 10.1112/plms.12003. Download .pdf.
39. Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations . Advances in Nonlinear Analysis, 6, (2017), no. 2, 237-242. DOI: 10.1515/anona-2016-0267. Download .pdf.
40. The Hardy-Schrodinger operator with interior singularity: The remaining cases, with Nassif Ghoussoub. Calculus of Variations and PDEs, 56, (2017), Art.149; 54pp. Download .pdf.
41. Mass and asymptotics associated to fractional Hardy-Schr\ »odinger operators in critical regimes,
with N.Ghoussoub, S.Shakerian and M.Zhao. Communications in PDEs, DOI: 10.1080/03605302.2018.1476528. Download .pdf.
42. Examples of sharp asymptotic profiles of singular solutions to an elliptic equation with a sign-changing non-linearity, with F.Cirstea and J.Vetois. Mathematische Annalen, 375, (2019), 1193-1230. Download .pdf. The online version.
43. The Hardy–Schrödinger operator on the Poincaré ball: Compactness, multiplicity, and stability of the Pohozaev obstruction, with N.Ghoussoub and S.Mazumdar. Journal of Differential Equations, 320, (2022), 510-557. Download .pdf.
44. Multiplicity and stability of the Pohozaev obstruction for Hardy-Schrödinger equations with boundary singularity, with N.Ghoussoub and S.Mazumdar. Memoirs of the AMS, 285, Number 1415, (2023), 1-112. Download .pdf.
45. Blowing-up solutions for second-order critical elliptic equations: the impact of the scalar curvature, with J.Vétois IMRN, 2, (2023), 901-931. Download the extended or the short version.
46. Concentration analysis for elliptic critical equations with no boundary control: ground-state blow-up, with H.Mesmar, DCDS,  Issue in honor of Professor Yihong Du’s 60th birthday. (2024), 17(4): 1599-1620.
47. Extremal functions for twisted sharp Sobolev inequalities with lower-order remainder terms. The high dimensional case, with Olivier Druet and Emmanuel Hebey, Preprint, (2024).
48. One-bubble nodal blow-up for asymptotically critical stationary Schrödinger-type equations, avec Bruno Premoselli, Preprint, (2024).

Videos

05/2017: The Hardy-Schrodinger operator with interior singularity: mass and blow-up analysis. Talk given on May 24th 2017 at la Casa Matematica Oaxaca (CMO), BIRS center, Mexico.
11/2017: Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign-changing nonlinearity . Talk given on November 17th 2017 at the First Belgium-Chile-Italy Confeence in PDEs, Bruxelles.
05/2019: Hardy-Sobolev critical equation with boundary singularity: multiplicity and stability of the Pohozaev obstruction. Talk given omn May 8th at the Banff International Research Station (BIRS), Canada.

Talks and conferences:

12/2000: Series of talks at the University of Rome III (Italy).
02/2001: PDE seminar, University of Cergy-Pontoise (France).
03/2001: Analysis seminar, University of Amiens (France).
01/2002: Geometry seminar, University of Nancy (France).
01/2002: Analysis seminar, University of Tours (France).
02/2002: Mathematics Colloquium, Tata Institute, Bangalore (Inde).
03/2002: Series of talks at the University of Rome III (Italy).
10/2002: Analysis seminar, ETH Zurich (Switzerland).
01/2003: Colloquium, University of Fribourg (Switzerland).
02/2003: PDEs and Geometry seminar, Notre Dame University (USA).
02/2003: Geometric Analysis seminar, Princeton University (USA).
03/2003: Geometry and Analysis seminar, University of Nice (France).
04/2003: Complex Geometry seminar, University of Marseille I (France).
06/2003: Department seminar, University of La Rochelle (France).
08/2003: Conference on Partial Differential equations, Oberwolfach (Germany).
09/2003: Conference on Affine Geometry, Bedlewo (Poland).
01/2004: Analysis seminar, University of Amiens (France).
01/2004: Analysis seminar, ETH Zurich (Switzerland).
03/2004: PDEs and applications seminar, ENS Lyon (France).
11/2004: Differential Geometry and PDE seminar, University of British Columbia, Vancouver (Canada).
03/2005: Conference « Recent Advances in Calculus of Variations and PDE’s », Pisa (Italy).
05/2005: Conference « Analytic Aspects of Problems in Riemannian Geometry », Brest (France).
09/2005: Conference « Interactions between Complex Geometry and Real Analysis », Hanover (Germany).
11/2005: Complex Geometry seminar, University of Marseille I (France).
02/2006: Analysis seminar, University of Reims (France).
02/2006: Differential Geometry and PDE seminar, University of British Columbia, Vancouver (Canada).
03/2006: Series of graduate courses at the University of Wisconsin, Madison (USA).
03/2006: Geometric Analysis Seminar, University of Wisconsin, Madison (USA).
04/2006: Analysis Seminar, ETH Zurich (Switzerland).
05/2006: Differential Equations Seminar, University of Rome II (Italy).
05/2006: Seminar, University of Rome III (Italy).
06/2006: Analysis Seminar, University of Warwick (England).
06/2006: AIMS Conference, Poitiers (France).
12/2006: Algebra and Geometry Seminar, University of Brest (France).
01/2007: Differential Geometry and Analysis Semianr, University of Magdeburg (Germany).
01/2007: Analysis seminar, University of Amiens (France).
02/2007: Lecture series in PDE, Chinese University of Hong-Kong (Hong-Kong)
02/2007: Colloquium, Chinese University of Hong-Kong (Hong-Kong)
08/2007: Conference « Loss of compactness in nonlinear PDE: Recent trends », Banff (Canada).
11/2007: Colloquium, Australian National University, Canberra (Australia).
01/2008: MIP seminar, University of Toulouse III (France).
02/2008: Analysis seminar, SISSA, Trieste (Italie).
06/2008: Second Canada-France Mathematical Congress 2008, Montréal (Canada).
06/2008: Conference « Conformal Geometry: invariant theory and the variational method », Roscoff (France).
10/2008: Complex geometry seminar, University of Marseille I (France).
11-12/2008: Series of lectures at the Technic University of Berlin (Germany).
01/2009: « Journées Nancéiennes de Géométrie », University of Nancy I (France).
02/2009: Geometric Analysis seminar, Albert-Einstein-Institute, Potsdam, (Germany).
04/2009: Analysis seminar, ETH Zurich (Switzerland).
07/2009: Conference « Asymptotic analysis in the calculus of variations and PDEs », University of British Columbia, Vancouver (Canada).
09/2009: Conference « Workshop in Nonlinear Elliptic PDEs » for Jean-Pierre Gossez’s 65th birthday, Free University of Bruxelles (Belgium).
10/2009: Conference  » Problèmes non linéaires avec perte de compacité: perspectives et applications », Luminy (France).
10/2009: Geometry and Analysis seminar, University of Nice (France).
10/2009: Interregional Colloquium, University of Saabrucken (Germany).
11/2009: Analysis seminar, Chinese University of Hong-Kong (Hong-Kong).
12/2009 : Analysis, Geometry and Algebra seminar, University of Metz (France).
04/2010: Series of talks, Tata Institute, Bangalore (Inde).
06/2010: Geometry and Analysis seminar, University of Nice (France).
07/2010: France-Asia Summer school « Singularities in pdes », IHES (France).
11/2010: Series of talks, University of Sydney (Australia).
11/2010: Analysis and PDE seminar, Australian National University, Canberra (Australia).
05/2011: Analysis Seminar, Universitaet zu Koeln (Germany).
05/2011: Conference « Higher Order equations in Geometry and Physics », SISSA, Trieste (Italy).
06/2011: Conference « Recent Advances on Elliptic Issues », Université de Besancon (France).
01/2012: Conference « Cocompact imbeddings and profile decomposition », TIFR Bangalore (India).
05/2012: Conference « Workshop on Nonlinear Partial Differential Equations to celebrate the sixtieth birthday of Patrizia Pucci », Universita degli Studi di Perugia (Italy).
06/2012: Conference « Higher order problems in geometric analysis », University of Bath (England).
06/2012: Algebra and Analysis seminar, Université de Brest (France).
11/2012: Analysis seminar, Chinese University of Hong-Kong.
11/2012: Conference « Geometric PDEs », Paris (France).
11/2012: Conference « Singular limit problems in nonlinear PDEs », CIRM, Marseille (France).
04/2013: PDE seminar, Pontificia Universidad Catolica de Chile, Santiago.
07/2013: Conference « Nonlinear PDEs, Functional Analysis and Applications: in celebration of Nassif Ghoussoub’s 60th birthday », Vancouver (Canada).
10/2013: PDE seminar, University of British Columbia, Vancouver (Canada).
12/2013: Conference « Geometric Variational Problems », Banff (Canada).
03/2014: Differential Geometry/PDE seminar, University of Washington, Seattle (USA).
05/2014: Conference « Geometric Aspects of Semilinear Elliptic and Parabolic Equations: recent Advances and Future Perspectives », Banff (Canada).
06/2014: Conference « Rencontre Nicoise d’Analyse Géométrique en l’honneur de Philippe Delanoe », Nice (France).
06/2014: Conference « PDEs in Geometry and Physics », University of Notre-Dame (USA).
11/2014: Analysis Seminar, Universitaet Basel (Switzerland).
02/2015: Nonlinear Analysis and PDE seminar, Université Libre de Bruxelles (Belgium).
04/2015: PDE Seminar, University of Sydney (Australie).
04/2015: PDE Seminar, University of Wollongong (Australie).
05/2015: Geometry Symposium, Université de Brest (France).
06/2015: Conference « New Trends on Concentration Phenomena in Nonlinear Elliptic Equations », Lyon (France).
02/2016: Geometric Analysis seminar, McGill University, Montréeal (Canada).
11/2016: PDE seminar, University of Sydney (Australia).
11/2016: International conference on nonlinear partial differential equations, A celebration of Professor Norman Dancer’s 70th birthday, University of New England, Armidale (Australia).
05/2017: PDE Workshop ULB-UCL, Université Catholique de Louvain (Belgique).
05/2017: Conference « Geometric Properties of Local and non-Local PDEs », Oaxaca (Mexico).
06/2017: Rencontre d’Analyse Géométrique, University of Nice (France).
06/2017: Conference « Nonlinear Analysis in Rome », University of Notre Dame in Rome (Italy).
11/2017: Conference « First Belgium+Chile+Italy conference in PDE », Université Libre de Bruxelles (Belgium).
03/2018: Workshop « Geometric Analysis », CRM Montréal (Canada).
05/2018: Conference on Positivity and Differential Equations, Köln (Deutschland).
11/2018: « A seminar day on elliptic problems », Nancy (France).
05/2019: Conférence « Nonlinear Geometric PDEs », Banff (Canada).
12/2019: Workshop « Journ\’ee FNRS », Bruxelles (Belgium).\par
05/2020: Geometric Online Seminar, McGill University (Montr\’eal).\par
05/2020: Conference « Geometric and Analytical Aspects of Nonlinear Elliptic Equations and Related Evolution Problems », Oaxaca BIRS (Mexico) (postponed).
12/2020: Conference « Geometric PDEs », Nouakchott (Mauritanie). Online.
06/2021: Conference « Canadian Mathematical Society 75+1th anniversary meeting », Ottawa (Canada) (online, initially scheduled in 2020).
09/2021: Conference « Geometric PDEs @ Caserta », Caserta (Italy) (initially scheduled in 2020).
09/2021: Conference «  »Three days of PDEs, friendship, love and nonlinearities »,  Pisa (Italy) (initially scheduled in 2020).
09/2021: Conference « Nonlinear Potential Theoretic Methods in Partial Differential Equations », Banff (Canada) (online).
05/2022: Seminar, Universita degli studi Roma 3 (Italia).
11/2022: Conference « Nonlinear PDEs and applications, a celebration of  Yihong Du’s 60th birthday », Sydney (Australia).
06/2023: Conference « Sobolev inequalities in the Alps », Grenoble (France).
05/2024: Workshop « Analysis of Geometric Singularities », CRM Montréal (Canada).

Invitations in foreign universities:

12/2000: Universita di Roma III (Italy).
02/2002: Tata Institute, Bangalore (India).
03/2002: Universita di Roma III (Italy).
02/2003: Notre Dame University (USA).
02/2003: Princeton University (USA).
01/2004: ETH Zurich (Switzerland).
11/2004: University of British Columbia, Vancouver (Canada).
07/2005: University of British Columbia, Vancouver (Canada).
02/2006: University of British Columbia, Vancouver (Canada).
03/2006: University of Wisconsin at Madison (USA).
04/2006: ETH Zurich (Switzerland).
05/2006: Universita de Roma II (Italy).
01/2007: Universitaet Magdeburg (Germany).
02/2007: Chinese University of Hong-Kong (Hong-Kong).
05/2007: Universita di Perugia (Italy).
08/2007: University of British Columbia, Vancouver (Canada).
11/2007: Australian National University, Canberra (Australia).
02/2008: Chinese University of Hong-Kong (Hong-Kong).
06/2008: McGill University, Montréal (Canada).
11/2008: Universita de Roma II (Italy).
02/2009: Technische Universitaet, Berlin (Germany).
02/2009: Universitaet Magdeburg (Germany).
04/2009: ETH Zurich (Switzerland).
07/2009: University of British Columbia, Vancouver (Canada).
11/2009: Chinese University of Hong-Kong (Hong-Kong).
04/2010: Tata Institute, Bangalore (India).
04/2009: Chinese University of Hong-Kong (Hong-Kong).
11/2009: University of Sydney (Australia).
08/2011: Universitaet Magdeburg (Germany).
10/2011: Chinese University of Hong-Kong (Hong-Kong).
08/2012: McGill University, Montréal (Canada).
11/2012: Chinese University of Hong-Kong (Hong-Kong).
04/2013: Pontificia Universidad Catolica de Chile, Santiago.
04/2015: University of Sydney (Australia).
02/2016: McGill University, Montréal (Canada).
07/2016: University of British Columbia, Vancouver (Canada).
11/2016: University of Sydney (Australia).
02/2020: University of British Columbia (Canada).
06/2020: McGill University, Montréal (Canada) (canceled).
11/2022: University of Sydney (Australia).
05/2024: McGill University, Montréal (Canada).