标题： 任务$p<n-1$：可能的——超越常规极限的非线性弹性 显示英文标题

标题： Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits

摘要： 本文首次证明了非线性弹性模型中 Neohookean 型能量的下半连续性，该模型允许 $p < n-1$ 的下半连续性。 我们允许的变形类由 Sobolev $W^{1,p}$ 同胚的弱极限组成。 我们还通过研究在某些点处可以形成空腔的同胚的弱极限，引入了一个允许空腔的模型。 在该模型中，我们将所创建表面的测度添加到能量泛函中，并再次证明了该泛函的下半连续性。 显示英文摘要

摘要： In this paper we prove the lower semicontinuity of a Neohookean-type energy for a model of Nonlinear Elasticity that allows, for the first time, for $p<n-1$. Our class of admissible deformations consists of weak limits of Sobolev $W^{1,p}$ homeomorphisms. We also introduce a model that allows for cavitations by studying weak limits of homeomorphisms that can open cavities at some points. In this model we add the measure of the created surface to the energy functional and for this functional we again prove lower semicontinuity.