2020
DOI: 10.1016/j.jfa.2020.108658
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Injectivity almost everywhere for weak limits of Sobolev homeomorphisms

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Cited by 14 publications
(8 citation statements)
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“…Property (vi) for limits of Sobolev homeomorphisms follows by [5], see also [44,Lemma 3.4] and [43,Theorem 10]. Finally, the Lusin N -property, a.e.…”
Section: Closure Of Admissible Deformationsmentioning
confidence: 90%
“…Property (vi) for limits of Sobolev homeomorphisms follows by [5], see also [44,Lemma 3.4] and [43,Theorem 10]. Finally, the Lusin N -property, a.e.…”
Section: Closure Of Admissible Deformationsmentioning
confidence: 90%
“…While Theorem 1.3 (and in turn our Theorem 1.1) follows by an adaptation of the arguments in the seminal work by Müller and Spector [12], Bouchala, Hencl, and Molchanova [4] also provide an example of the limit case p = n − 1, where a theorem such as Theorem 1.3 completely fails. Namely they show Theorem 1.4 (Bouchala, Hencl, Molchanova).…”
mentioning
confidence: 87%
“…Observe that for s ≤ n−1 n the above statements hold trivially. This note is inspired by the recent work by Bouchala, Hencl, and Molchanova [4] who proved a corresponding result for s = 1.…”
mentioning
confidence: 89%
See 1 more Smart Citation
“…Almost everywhere injectivity of deformations has been analyzed in [10] for limits of Sobolev homeomorphisms, in [47] in the presence of distorsion penalizations (see, e.g., [42,49]), and in [40] for second-grade non-simple materials (cf. [54,55]), whereas a first numerical implementation of the Ciarlet-Nečas condition as an energy penalization has been exploited in [46] in the setting of finite strain elastoplasticity.…”
Section: Introductionmentioning
confidence: 99%