Injectivity almost everywhere for weak limits of Sobolev homeomorphisms

Abstrakt

Let Omega subset of R-n be an open set and let f is an element of W-1,W-p(Omega, 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 <= 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 the topological image of a point is a continuum for every point in a set of positive measure in the domain. (C) 2020 Elsevier Inc. All rights reserved.

Klíčová slova

• Injectivity
• almost
• everywhere
• for
• weak
• limits
• Sobolev
• homeomorphisms