Kavli Affiliate: Zheng Zhu
| First 5 Authors: Ondřej Bouchala, Stanislav Hencl, Zheng Zhu, ,
| Summary:
We prove that the key property in models of Nonlinear Elasticity which
corresponds to the non-interpenetration of matter, i.e. injectivity a.e., can
be achieved in the class of weak limits of homeomorphisms under very minimal
assumptions.
Let $Omegasubseteq mathbb{R}^n$ be a domain and let
$p>leftlfloorfrac{n}{2}rightrfloor$ for $ngeq 4$ or $pgeq 1$ for
$n=2,3$. Assume that $f_kin W^{1,p}$ is a sequence of homeomorphisms such that
$f_krightharpoonup f$ weakly in $W^{1,p}$ and assume that $J_f>0$ a.e. Then we
show that $f$ is injective a.e.
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