# Xavier Lamy

## Homepage

### Preprints

[36] * On C ^{1} regularity for degenerate elliptic equations in the plane*, with Thibault Lacombe.

[35] * On regularity and rigidity of 2×2 differential inclusions into non-elliptic curves*, with A. Lorent and G. Peng.

[34] * Optimal Quantitative Stability of the Möbius group of the sphere in all dimensions*, with A. Guerra and K. Zemas.

[33] * Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimension*, with A. Guerra and K. Zemas.

### Published articles

[32] * Generation of vortices in the Ginzburg-Landau heat flow*, with M. Kowalczyk. Ann. Inst. H. Poincaré Anal. Non Linéaire, 2023.

[31] * On Lebesgue points of entropy solutions to the
eikonal equation*, with E. Marconi.
Proc. Roy. Soc. Edinburgh Sect. A, 2023.

[30] * Stability of the vortex in micromagnetics and related models*, with E. Marconi.
Ann. Sc. Norm. Super. Pisa Cl. Sci., 2023.

[29] * Quantitative rigidity of differential inclusions in two dimensions*, with A. Lorent and G. Peng.
Int. Math. Res. Not. IMRN, 2023.

[28] * On optimal regularity estimates for finite-entropy solutions of
scalar conservation laws*, with A. Lorent and G. Peng. C. R., Math., Acad. Sci. Paris, 2023.

[27] * Far-field expansions for harmonic maps and the electrostatics analogy in nematic suspensions*, with S. Alama, L. Bronsard and R. Venkatraman. J. Nonlinear Sci., 2023.

[26] * On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds*, with A. Lorent and G. Peng. Comm. Partial Differential Equations, 2022.

[25] * Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system*, with M. Kowalczyk and P. Smyrnelis. Arch. Ration. Mech. Anal, 2022.

[24] * Singular perturbation of manifold-valued maps with anisotropic energy*, with A. Contreras. Anal. PDE, 2022.

[23] * Generalized characteristics for finite entropy solutions of Burgers' equation*, with A. Contreras Hip and E. Marconi. Nonlinear Anal., 2022.

[22] * On the stability of radial solutions to an anisotropic Ginzburg-Landau equation*, with A. Zúñiga. SIAM J. Math. Anal., 2022.

[21] * Saturn ring defect around a spherical particle immersed in nematic liquid crystal*, with S. Alama, L. Bronsard and D. Golovaty. Calc. Var. Partial Differential Equations, 2021.

[20] * On the L² stability of shock waves for finite entropy solutions of Burgers*, with A. Contreras Hip. J. Differential Equations, 2021.

[19] * Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture*, with A. Lorent and G. Peng. Arch. Ration. Mech. Anal, 2020.

[18]
*Global uniform estimate for the modulus of 2D Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy*, with R. Ignat and M. Kurzke. SIAM J. Math. Anal., 2020.

[17] * Optimal Besov differentiability for entropy solutions of the eikonal equation*, with F. Ghiraldin. Comm. Pure Appl. Math., 2020.

[16]
*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.*, with R. Ignat. Calc. Var. Partial Differential Equations, 2019.

[15] *On the convergence of minimizers of singular perturbation functionals*, with A. Contreras and R. Rodiac. Indiana Univ. Math. J., 2018.

[14] *Regularity of solutions to scalar conservation laws with a force*, with B. Gess. Ann. Inst. H. Poincaré Anal. Non Linéaire, 2018.

[13] *On the regularity of weak solutions to Burgers' equation with finite entropy production*, with F. Otto. Calc. Var. Partial Differential Equations, 2018.

[12] * Spherical particle in nematic liquid crystal under an external field: the Saturn ring regime *, with S. Alama and L. Bronsard. J. Nonlinear Sci., 2018.

[11] *Biaxial escape in nematics at low temperature*, with A. Contreras. J. Funct. Anal., 2017.

[10] * Minimizers of the Landau-de Gennes energy around a spherical colloid particle *, with S. Alama and L. Bronsard. Arch. Ration. Mech. Anal, 2016.

[9] * Analytical description of the Saturn-ring defect in nematic colloids *, with S. Alama and L. Bronsard. Phys. Rev. E, 2016.

[8] * Boundary regularity of weakly anchored harmonic maps *, with A. Contreras and R. Rodiac. C. R. Math. Acad. Sci. Paris, 2015.

[7] *Vortex structure in p-wave superconductors*, with
S. Alama and L. Bronsard. J. Math. Phys, 2015.

[6] *Persistence of superconductivity in thin shells beyond Hc1*, with A. Contreras. Commun. Contemp. Math., 2015.

[5] *Characterization of function spaces via low regularity mollifiers*, with P. Mironescu. Discrete Contin. Dyn. Syst. Ser. A, 2015.

[4] *Uniaxial symmetry in nematic liquid crystals*. Ann. Inst. H. Poincaré Anal. Non Linéaire, 2015.

[3] *Bifurcation analysis in a frustrated nematic cell*. J. Nonlinear Sci., 2014.

[2] *Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains*, with P. Mironescu. J. Math. Pures Appl., 2014.

[1]
*Some properties of the nematic radial hedgehog in the Landau–de Gennes theory*. J. Math. Anal. Appl., 2013.

### Habilitation manuscript

*Some contributions to the mathematical analysis of liquid crystal and line-energy models*

### Thesis manuscript

*Autour des singularités d'applications vectorielles en physique de la matière condensée*