Xavier Lamy

collaborators

6 papers

math.AP2026

Some lifting and approximation properties for maps in $W^{1, 2} (B^{3}; S^{2})$

AndrÃ© Guerra, Xavier Lamy, Konstantinos Zemas

Smooth maps $u : B^{3} \to S^{2}$ can be lifted to $u^: B^{3} \to S^{3}$ using the Hopf fibration $h : S^{3} \to S^{2}$ via the factori…

math.AP2026

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves

Xavier Lamy, Andrew Lorent, Guanying Peng

We study differential inclusions $D u \in I^$ in an open set $I^c ◯ \subset R^{2}$ , where $I^\subset R^{2 \times 2}$ is a compact connected $C^{2}$ curve without rank-one conne…

math.AP2026

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

AndrÃ© 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

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

Xavier Lamy, Elio Marconi

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

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_Ï(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsy…

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 $m : I^c ◯ \subset R^{2} \to R^{2}$ such that $∣ m ∣ = 1$ a.e. and $div m = 0$ in $\ma…

Some lifting and approximation properties for maps in W1,2(B3;S2)

On regularity and rigidity of 2×2 differential inclusions into non-elliptic curves

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

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

The conformal limit for bimerons in easy-plane chiral magnets

Another regularizing property of the 2D eikonal equation

Some lifting and approximation properties for maps in $W^{1, 2} (B^{3}; S^{2})$

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves