单边极小性质稳定性的$Γ$ -收敛方法

Deterministic homogenization of variational inequalities with unilateral constraints

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each scale a large set of concrete deterministic behavior such as the periodic, the almost periodic, the convergence at infinity. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is of the same type as the problem with rapidly oscillating coefficients.

凸集的 Mosco 收敛与具有自然增长低阶项的微分算子单边问题

Mosco-convergence of convex sets and unilateral problems for differential operators with lower order terms having natural growth

本文研究障碍型凸集上变分不等式解在 Mosco 收敛下的稳定性，证明含自然增长低阶项的 Leray-Lions 型算子问题的解对约束集收敛保持稳定，推广了经典稳定性结果。

障碍问题的Bregman近端点分析

Analysis of Bregman Proximal Point for the Obstacle Problem

本文分析障碍问题的Bregman近端点方法，建立子问题的适定性，基于序列严格局部极小性推导H^1范数下的次线性及线性收敛速率，并证明其尖锐性。

脆性材料中准静态断裂演化的线性化

Linearization of quasistatic fracture evolution in brittle materials

本文证明非线性弹性准静态断裂演化在刚度趋于无穷时收敛到线性弹性准静态裂纹扩展解，无需裂纹几何先验假设，推广了静态线性化结果至演化情形。

Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups

We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $Γ$-liminf of the rescaled energy in terms of the horizontal perimeter.

椭圆变分不等式的一个收敛准则

A Convergence Criterion for Elliptic Variational Inequalities

本文针对Hilbert空间中带单侧约束的椭圆变分不等式，提出了保证序列收敛于唯一解的充分必要条件，并应用于恢复适定性结果及解决热传导与弹性无摩擦接触问题。