Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes

Bi-Sobolev mappings f : Ω ⊂ R 2 → onto Ω ′ ⊂ R 2 have been defined as those homeomorphisms such that f and f − 1 belong to W loc 1 , 1 . We deduce regularity properties of the distortion of f from the regularity of the differential matrix D f − 1 and conversely.