Andrew Lorent

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20102022

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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.AP2016

Regularity of the Eikonal equation with two vanishing entropies

Andrew Lorent, Guanying Peng

The Aviles-Giga functional $I_{ε} (u) = \int_{Ω} \frac{∣ 1 - ∣ \nabla u ∣ ^{2} ∣ ^{2}}{ε} + ε \nabla^{2} u^{2} d x$ is a well known second order functional that models phe…

math.AP2010

A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity

Andrew Lorent

The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magne…