Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity

Injectivity almost everywhere for weak limits of Sobolev homeomorphisms

Let $Ω\subset\mathbb{R}^n$ be an open set and let $f\in W^{1,p}(Ω,\mathbb{R}^n)$ be a weak (sequential) limit of Sobolev homeomorphisms. Then $f$ is injective almost everywhere for $p>n-1$ both in the image and in the domain. For $p\leq n-1$ we construct a strong limit of homeomorphisms such that the preimage of a point is a continuum for every point in a set of positive measure in the image and a topological image of a point is a continuum for every point in a set of positive measure in the domain.

关于二阶梯度非线性弹性力学中单射性的注记

Note on injectivity in second-gradient Nonlinear Elasticity

本文研究二阶梯度非线性弹性中平面映射的单射性，证明在边界同胚及 Jacobian 可积性条件下映射为同胚，并给出条件精确性及零 Jacobian 集合投影测度的新结果。

具有 $p$-可积扭曲的映射的雅可比行列式倒数的全局可积性

Global Integrability of the Reciprocal of Jacobians for Homeomorphisms of Finite Distortion

研究了有限扭曲映射雅可比行列式倒数的全局可积性，并加强了关于弱极限的 Sobolev 映射结果。

Sobolev 同胚的弱极限是一对一的

Weak limits of Sobolev homeomorphisms are one to one

本文在极小假设下证明非线性弹性中物质不可穿透性对应的几乎处处单射性可由 Sobolev 同胚弱极限保持，从而给出弱极限仍为几乎处处单射的充分条件。

具有弱正则性的 BGG 序列及其应用

BGG sequences with weak regularity and applications

本文研究了 Sobolev 框架下的 BGG 复形，在无需代数单射/满射条件下计算了共形变形与共形 Hessian 复形的上同调，并应用于建立共形 Korn 不等式及揭示 Cosserat 弹性模型与 Hodge-Laplacian 问题的联系。