My habilitation thesis "Singularités des champs de vecteurs
à divergence nulle et à valeurs dans S^1 ou S^2.
Applications
en micromagnétisme" can be downloaded [HERE]
Preprints
1.
Renormalised energy between boundary vortices in thin-film
micromagnetics with Dzyaloshinskii-Moriya interaction,
arXiv:2401.17830 (with F. L'Official) [pdf]
2.
Minimality of vortex solutions to Ginzburg-Landau type systems for
gradient fields
in the unit ball in dimension N ≥ 4, arXiv:2310.11384
(with M. Nahon, L. Nguyen) [pdf]
Publications
52.
Vortex sheet solutions for the Ginzburg-Landau system in cylinders:
symmetry and global minimality,
accepted in Calc. Var. Partial
Differential Equations, 2023 (with M. Rus) [pdf]
51.
An effective model for boundary vortices in thin-film micromagnetics,
Math. Models Methods Appl. Sci. 33 (2023), 1929-1973. (with M.
Kurzke) [pdf]
50.
Asymptotic stability of precessing domain walls for the
Landau-Lifshitz-Gilbert equation in
a nanowire with
Dzyaloshinskii-Moriya interaction, Comm. Math. Phys. 401 (2023),
2901-2957 (with R. Cote) [pdf]
49.
Local minimality of R^N -valued and S^N -valued Ginzburg–Landau
vortex solutions in the unit ball B^N,
online in
Ann. Inst. H. Poincaré, Anal. Non linéaire, 2023(with L. Nguyen)
[pdf]
48.
Uniqueness result for a weighted pendulum equation modeling domain
walls in notched ferromagnetic nanowires,
C. R. Math.
Acad. Sci. Paris 360 (2022), 819-828 [pdf]
47.
Separation of domain walls with nonlocal interaction and their
renormalised energy
by Γ-convergence in thin
ferromagnetic films, J. Differential Equations 339 (2022),
395-475 (with R. Moser) [pdf]
46.
Variational methods for a singular SPDE yielding the universality of
the magnetization ripple,
Comm.
Pure Appl. Math. 76 (2023), 2959-3043. (with F.Otto, T.
Ried, P. Tsatsoulis) [pdf]
45.
Renormalized energy between vortices in some Ginzburg-Landau models
on 2-dimensional Riemannian manifolds, Arch.
Ration. Mech. Anal. 239 (2021), 1577–1666
(with R. Jerrard) [pdf]
44.
Global Jacobian and Gamma-convergence in a two-dimensional
Ginzburg-Landau model for boundary vortices,
J. Funct.
Anal. 280 (2021), 66pp (with M. Kurzke) [pdf]
43.
Symmetry and multiplicity of solutions in a two-dimensional Landau-de
Gennes model for liquid crystals,
Arch.
Ration. Mech. Anal. 237 (2020),
1421-1473 (with L. Nguyen, V. Slastikov, A. Zarnescu)
[pdf]
42. A DeGiorgi type
conjecture for minimal solutions to a nonlinear Stokes
equation,
Comm.
Pure Appl. Math. 73 (2020), 771-854 (with A. Monteil)
[pdf]
41.
On the uniqueness of minimisers of Ginzburg-Landau functionals,
Ann.
Sci. Éc. Norm. Supér. 53 (2020), 589-613 (with L. Nguyen, V.
Slastikov, A. Zarnescu) [pdf]
40.
Global uniform estimate for the modulus of 2D Ginzburg-Landau
vortexless solutions
with asymptotically infinite boundary
energy,
SIAM J. Math. Anal. 52 (2020), 524-542 (with M.
Kurzke and X. Lamy) [pdf]
39.
A necessary condition in a De Giorgi type conjecture for elliptic
systems in infinite strips,
accepted in the volume dedicated to
Haim Brezis on the occasion of his 75th birthday,
Pure and
Applied Functional Analysis 5 (2020), 981-999 (with A. Monteil)
[pdf]
38.
Dimension reduction and optimality of the uniform state in a
Phase-Field-Crystal model
involving a higher order functional,
J. Nonlinear Sci. 30 (2020), 261-282 (with H. Zorgati)
[pdf]
37.
Energy minimisers of prescribed winding number in an S^1-valued
nonlocal Allen-Cahn type model,
Adv. Math. 357 (2019), 45 pp.
(with Roger Moser) [pdf]
36.
Lifting of RP^{d-1}-valued maps in BV and applications to uniaxial
Q-tensors.
With an appendix on an intrinsic BV-energy for
manifold-valued maps,
Calc. Var. Partial Differential Equations
58 (2019), no. 2, 26 pp (with X. Lamy) [pdf]
35.
The magnetization ripple: a nonlocal stochastic PDE perspective,
J.
Math. Pures Appl. (9) 130 (2019), 157-199 (with F. Otto)
[pdf]
34. Uniqueness
of degree-one Ginzburg-Landau vortex in the unit ball in dimensions N
≥ 7
C. R. Math. Acad. Sci. Paris 356 (2018), 922-926
(with L. Nguyen, V. Slastikov, A. Zarnescu) [pdf]
33.
Néel walls with prescribed winding number and how a nonlocal term
can change the energy landscape,
J. Differential Equations
263 (2017), 5846–5901 (with R. Moser)
[pdf]
32.
Interaction energy between vortices of vector fields on Riemannian
surfaces,
C. R. Math. Acad. Sci. Paris 355 (2017), 515–521
(with R. Jerrard) [pdf]
31.
Kinetic formulation of vortex vector fields,
Anal. PDE 10
(2017), 729–756 (with P. Bochard)
[pdf]
30.
Stability of point defects of degree ±1/2 in a two-dimensional
nematic liquid crystal model,
Calc. Var.
Partial Differential Equations 55 (2016), 33pp (with L.
Nguyen, V. Slastikov, A. Zarnescu) [pdf]
29. Interaction energy of domain
walls in a nonlocal Ginzburg-Landau type model from micromagnetics,
Arch.
Ration. Mech. Anal. 221 (2016), 419-485 (with R.
Moser) [pdf]
28. Asymmetric domain walls of small angle in soft
ferromagnetic films,
Arch.
Ration. Mech. Anal. 220 (2016), 889-936 (with L.
Doering) [pdf]
27. Instability of point defects in a two-dimensional nematic
liquid crystal model,
Ann. Inst. H. Poincaré, Anal. Non
linéaire 33 (2016), 1131–1152 (with L. Nguyen, V. Slastikov, A.
Zarnescu) [pdf]
26. A regularizing property of the 2D-eikonal
equation,
Comm. Partial Differential Equations 40 (2015),
1543–1557 (with C. De Lellis) [pdf]
25. Stability of the melting hedgehog in the Landau-de
Gennes theory of nematic liquid crystals
Arch.
Ration. Mech. Anal. 215 (2015), 633–673 (with
L. Nguyen, V. Slastikov, A. Zarnescu) [pdf]
24. A reduced model for domain walls in soft
ferromagnetic films at the cross-over from symmetric to asymmetric
wall types,
J.
Eur. Math. Soc. (JEMS) 16 (2014), 1377–1422.(with L.
Döring, F. Otto) [pdf]
23. Uniqueness results for an ODE related to a
generalized Ginzburg-Landau model for liquid crystals,
SIAM
Journal on Mathematical Analysis 46 (2014), 3390–3425 (with L.
Nguyen, V. Slastikov, A. Zarnescu) [pdf]
22. A thin-film limit in the Landau-Lifshitz-Gilbert
equation relevant for the formation of Néel walls,
The Haim
Brezis Festschrift, J. Fixed Point Theory Appl. 15 (2014) 241–272
(with R. Cote, E. Miot) [pdf]
21.
Stability of the vortex defect in the Landau–de Gennes theory for
nematic liquid crystals,
C.R. Acad. Sci. Paris, Ser. I 351
(2013) 533–537 (with L. Nguyen, V. Slastikov, A. Zarnescu)
[pdf]
20. Two-dimensional unit-length vector fields of
vanishing divergence,
J. Funct. Anal. 262 (2012),
3465–3494 [pdf]
19. A zigzag pattern in micromagnetics,
J.
Math. Pures Appl. 98 (2012), 139-159. (with R. Moser)
[pdf]
18. Singularities of divergence-free vector fields
with values into S^1 or S^2. Applications to micromagnetics,
Confluentes Mathematici 4 (2012), 1-80 [pdf]
17. Entropy method for line-energies,
Calc. Var.
Partial Differential Equations 44 (2012), 375-418 (with B.
Merlet) [pdf]
16. Gradient vector fields with values into S^1,
C.R. Acad. Sci. Paris, Ser. I 349 (2011), 883-887 [pdf]
15. A compactness result for Landau state in thin-film
micromagnetics,
Ann. Inst. H. Poincaré, Anal. Non linéaire
28(2011), 247-282 (with F. Otto) [pdf]
14.
Lower bound for the energy of Bloch walls in micromagnetics,
Arch.
Ration. Mech. Anal. 199 (2011), 369-406 (with B. Merlet)
[pdf]
13.
Vortex energy and 360° Néel walls in thin films micromagnetics,
Comm. Pure Appl. Math. 63 (2010), 1677-1724 (with H.
Knüpfer) [pdf]
12.
A Gamma-convergence result for Néel walls in micromagnetics,
Calc.
Var. Partial Differential Equations 36 (2009), 285-316.
[pdf]
11.
A survey of some new results in ferromagnetic thin films,
Séminaire
d'Équations aux Dérivées Partielles (Ecole Polytechnique)
2007--2008, Exp. No. VI, 19 pp. [pdf]
10.
A compactness result in thin-film micromagnetics and the optimality
of the Néel wall,
J. Eur. Math. Soc. (JEMS) 10 (2008),
909-956. (with F. Otto) [pdf]
9.
Pohozaev type
identities for an elliptic equation ,
CRM Proceedings and
Lecture Notes, 44 (2008), 75-88 [pdf]
8.
On the relation between minimizers of a Gamma-limit energy and
optimal lifting in BV-space ,
Commun. Contemp. Math
9 (2007), 447-472 (with A. Poliakovsky)
[pdf]
7.
Energy expansion
and vortex location for a two dimensional rotating Bose-Einstein
condensate,
Rev. Math. Phys. 18 (2006), 119--162
(with V. Millot) [pdf]
6.
The critical velocity for vortex existence in a two dimensional
rotating Bose-Einstein condensate,
J. Funct. Anal. 233(2006),
260-306 (with V. Millot) [pdf]
5.
Vortices in a 2d
rotating Bose-Einstein condensate,
C.R. Acad. Sci. Paris, Ser.I
340(2005), 571-576 (with V. Millot)
[pdf]
4.
The space BV(S^2,S^1) : minimal connection and optimal lifting,
Ann.
Inst. H. Poincaré, Anal. Non linéaire 22(2005), 283-302 [pdf,
ps ]
3.
Optimal lifting for BV(S^1,S^1),
Calc. Var. Partial
Differential Equations 23(2005), 83-96 [pdf]
2.
On an open problem about how to recognize constant functions,
Houston Journal of Mathematics 31(1), 2005, 285-304
[pdf]
1.
Lifting of BV functions with values in S^1,
C.R. Acad. Sci.
Paris, Ser.I 337 (2003), 159-164 (with J. Davila)
[pdf]
Book
1. Singularities in some variational problems,
VDM Verlag
Dr. Müller, Saarbrücken, 2010, 260pp [pdf]
[cover_book] .
Reports
5. A De Giorgi type conjecture for elliptic systems under the
divergence constraint,
Oberwolfach Reports, Volume 22/2020
(Calculus of Variations: A. Figalli, R.V. Kohn, T.Toro, N.
Wickramasekera). [pdf]
4. Some uniqueness results for minimisers of
Ginzburg-Landau functionals,
Oberwolfach Reports, Volume 20/2018
(Nonlinear Data: Theory and Algorithms) [pdf]
3. Interaction energy of domain walls of logarithmically
decaying tails in a nonlocal variational model,
Oberwolfach
Reports, Volume XX/2016 (Calculus of Variations: S. Brendle, A.
Figalli, R. Jerrard, N. Wickramasekera). [pdf]
2. Le prix Henri Poincaré pour Sylvia Serfaty,
Gaz.
Math. 135 (2013), 51–56 (with B. Helffer) [pdf]
1. Pattern formation in micromagnetics,
Oberwolfach
Reports, Volume 36/2012 (Calculus of Variations: C. De Lellis, G.
Huisken, R. Jerrard). [pdf]
Publications in Romanian Journals
4. Hamilton-Jacobi
Equations and Optimal
Control ,
Proceedings of the
International Conference on Nonlinear Operators, Differential
Equations and Applications, Cluj-Napoca, 2001, Seminar on fixed point
theory Cluj-Napoca, 3/2002, 239-248 (with A. Basson)
3. Sur les
Conjectures de Markus-Yamabe et de la Jacobienne ,
Séminaire de la Theorie de la
Meilleure Approximation, Convexite et Optimisation, Ed. Srima (2000),
125-141
2. About an
interesting sequence, Octogon, 1/2000, 173-180
1. A
generalization of convex and midconvex functions, Analysis,
Functional equations, Approximation and Convexity, Proceedings of the
Conference Held in Honor of Professor Elena Popoviciu on the Occasion
of her 75th Birthday, Ed. Carpatica (1999), 89-93