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Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space
Siberian Mathematical Journal. 2017. Vol. 58. No. 4. P. 649–662.
Given a homeomorphism $\varphi \in W^{1,M}$ , we determine the conditions that guarantee the belonging of the inverse of $\varphi$ in some Sobolev–Orlicz space $W^{1,F}$ . We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev–Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev–Orlicz spaces which is defined by the first pair.