Xavier Lamy

Preprints

[37] On the existence of degenerate solutions of the two-dimensional H-system, with A. Guerra and K. Zemas.

[36] On C¹ 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