Xavier Lamy

activity

20232026

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4 papers · 1 filter

math.AP2025

Rectifiability of entropy productions for weak solutions of the 2D eikonal equation with supercritical regularity

Xavier Lamy, Elio Marconi

Weak solutions $m : Ω \subset R^{2} \to R^{2}$ of the eikonal equation \begin{align*} |m|=1\text{ a.e. and }\mathrm{div}\: m =0\,, \end{align*} arise naturally as shar…

math.AP2025

Global minimality of the Hopf map in the Faddeev-Skyrme model with large coupling constant

André Guerra, Xavier Lamy, Konstantinos Zemas

We prove that, modulo rigid motions, the Hopf map is the unique minimizer of the Faddeev--Skyrme energy in its homotopy class, provided that the radius of the target 2-sphere is no…

math.AP2025

The conformal limit for bimerons in easy-plane chiral magnets

Bin Deng, Radu Ignat, Xavier Lamy

We study minimizers $m : R^{2} \to S^{2}$ of the energy functional \begin{align*} E_σ(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsym…

math.AP2025

Another regularizing property of the 2D eikonal equation

Xavier Lamy, Andrew Lorent, Guanying Peng

A weak solution of the two-dimensional eikonal equation amounts to a vector field $m : Ω \subset R^{2} \to R^{2}$ such that $∣ m ∣ = 1$ a.e. and $div m = 0$ in $\mat…