Abstract
AbstractIn this paper, we consider refined geometric characterizations of weak p-quasiconformal mappings $$\varphi :\Omega \rightarrow \widetilde{\Omega }$$ φ : Ω → Ω ~ , where $$\Omega$$ Ω and $$\widetilde{\Omega }$$ Ω ~ are domains in $${\mathbb {R}}^n$$ R n . We prove that mappings with bounded geometric p-dilatation on the set $$\Omega {{\setminus }} S$$ Ω \ S , where S is a set with $$\sigma$$ σ -finite $$(n-1)$$ ( n - 1 ) -measure, are Sobolev $$W^1_{p,\text {loc}}$$ W p , loc 1 -mappings and generate bounded composition operators on Sobolev spaces.
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