G. Peng

activity

20142026

most citedRigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture

7 citations · 13 across the 15 of their papers we have counts for

collaborators

16 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

Nonexistence of a class of $T_{N}$ configurations for a hyperbolic system with one entropy

Guanying Peng, Anthony Vuolo

In Kirchheim, Müller and Šverák [Studying nonlinear PDE by geometry in matrix space. Geometric analysis and nonlinear partial differential equations, 2003], the authors proposed th…

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…

math.AP2021

Factorization for entropy production of the Eikonal equation and regularity

Andrew Lorent, Guanying Peng

The Eikonal equation arises naturally in the limit of the second order Aviles-Giga functional whose $Γ$ -convergence is a long standing challenging problem. The theory of entropy so…

math.AP2019★ 7 cited

Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture

Xavier Lamy, Andrew Lorent, Guanying Peng

In this paper we prove sharp regularity for a differential inclusion into a set $K \subset R^{2 \times 2}$ that arises in connection with the Aviles-Giga functional. The set…

math.AP2019★ 1 cited

On the Rank- $1$ convex hull of a set arising from a hyperbolic system of Lagrangian elasticity

Andrew Lorent, Guanying Peng

We address the questions (P1), (P2) asked in Kirchheim-Müller-Šverák (2003) concerning the structure of the Rank- $1$ convex hull of a submanifold $\mathcal{K}_1\subset M^{3\times 2…

math.AP2019

First critical field of highly anisotropic three-dimensional superconductors via a vortex density model

Andres Contreras, Guanying Peng

We analyze a mean field model for $3$ d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $G amma$ -…

math.AP2018★ 4 cited

Null Lagrangian Measures in subspaces, compensated compactness and conservation laws

Andrew Lorent, Guanying Peng

Compensated compactness is an important method used to solve nonlinear PDEs. A simple formulation of a compensated compactness problem is to ask for conditions on a set $\mathcal{K…

math.AP2017

Bounded solutions for a class of Hamiltonian systems

Philip Korman, Guanying Peng

We obtain bounded for all $t$ solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on $(- L, L)$ , with $L \rightarrow \inft…

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.AP2016

Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near $H_{c_{1}}$

Guanying Peng

We analyze minimizers of the Lawrence-Doniach energy for three-dimensional highly anisotropic superconductors with layered structure. For such a superconductor occupying a bounded…

math.AP2014★ 1 cited

Analysis of Minimizers of the Lawrence-Doniach Energy for Superconductors in Applied Fields

Patricia Bauman, Guanying Peng

We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder, $Ω \times [0, L]$ , in $R^{3}$ , where $Ω$ is a bounde…

On Aviles-Giga limit states with Lp entropy productions

Another regularizing property of the 2D eikonal equation

Nonexistence of a class of TN​ configurations for a hyperbolic system with one entropy

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

Factorization for entropy production of the Eikonal equation and regularity

Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture

On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity

First critical field of highly anisotropic three-dimensional superconductors via a vortex density model

Null Lagrangian Measures in subspaces, compensated compactness and conservation laws

Bounded solutions for a class of Hamiltonian systems

Regularity of the Eikonal equation with two vanishing entropies

Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near Hc1​​

Analysis of Minimizers of the Lawrence-Doniach Energy for Superconductors in Applied Fields

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

Nonexistence of a class of $T_{N}$ configurations for a hyperbolic system with one entropy

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

On the Rank- $1$ convex hull of a set arising from a hyperbolic system of Lagrangian elasticity

Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near $H_{c_{1}}$