A. Lorent

activity

20082026

most citedRegularity of sets with quasiminimal boundary surfaces in metric spaces

46 citations · 62 across the 16 of their papers we have counts for

collaborators

20 papers

math.AP2026

On Aviles-Giga limit states with $L^{p}$ entropy productions

Xavier Lamy, Andrew Lorent, Guanying Peng

The Aviles-Giga energy provides sequences of maps converging to weak solutions $m : Ω \subset R^{2} \to R^{2}$ of the eikonal equation \begin{align*} \mathrm{div}\, m=0\…

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…

math.AP2024

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

Xavier Lamy, Andrew Lorent, Guanying Peng

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

math.AP2022

Quantitative rigidity of differential inclusions in two dimensions

Xavier Lamy, Andrew Lorent, Guanying Peng

For any compact connected one-dimensional submanifold $K \subset R^{2 \times 2}$ which has no rank-one connection and is elliptic, we prove the quantitative rigidity estimate…

math.AP2022

On optimal regularity estimates for finite-entropy solutions of scalar conservation laws

Xavier Lamy, Andrew Lorent, Guanying Peng

We consider finite-entropy solutions of scalar conservation laws $u_{t} + a (u)_{x} = 0$ , that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Unde…

math.AP2022

On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds

Xavier Lamy, Andrew Lorent, Guanying Peng

Given any strictly convex norm $∥ \cdot ∥$ on $R^{2}$ that is $C^{1}$ in $R^{2} ∖ {0}$ , we study the generalized Aviles-Giga functional \[I_ε(m):=\int_Ω \left(ε…

On Aviles-Giga limit states with Lp entropy productions

Another regularizing property of the 2D eikonal equation

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

Quantitative rigidity of differential inclusions in two dimensions

On optimal regularity estimates for finite-entropy solutions of scalar conservation laws

On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds

On Aviles-Giga limit states with $L^{p}$ entropy productions

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