We prove that if a bilipschitz mapping is in then the inverse is also a class mapping. Further we prove that the class of bilipschitz mappings belonging to is closed with respect to composition and multiplication without any restrictions on . These results can be easily extended to smooth -dimensional Riemannian manifolds and further we prove a form of the implicit function theorem for Sobolev mappings.
Cite this article
Daniel Campbell, Stanislav Hencl, František Konopecký, The Weak Inverse Mapping Theorem. Z. Anal. Anwend. 34 (2015), no. 3, pp. 321–342