Abstract
We prove that if a bilipschitz mapping f is in W-loc(m,p) (R-n; R-n) then the inverse f(-1) is also a W-loc(m,p) (R-n; R-n) is class mapping. Further we prove that the class of bilipschitz mappings belonging to W-loc(m,p) (R-n;R-n) is closed with respect to composition and multiplication without any restrictions on m,p }= 1.
These results can be easily extended to smooth n-dimensional Riemannian manifolds and further we prove a form of the implicit function theorem for Sobolev mappings.