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- W3199438302 abstract "In this paper we study approximations of functions of Sobolev spaces Wp,loc2(Ω), Ω⊂Rn, by Lipschitz continuous functions. We prove that if f∈Wp,loc2(Ω), 1≤p<∞, then there exists a sequence of closed sets {Ak}k=1∞,Ak⊂Ak+1⊂Ω, such that the restrictions f|Ak are Lipschitz continuous functions and capp(S)=0, S=Ω∖⋃k=1∞Ak. Using these approximations we prove the change of variables formula in the Lebesgue integral for mappings of Sobolev spaces Wp,loc2(Ω;Rn) with the Luzin capacity-measure N-property." @default.
- W3199438302 created "2021-09-27" @default.
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- W3199438302 date "2022-02-01" @default.
- W3199438302 modified "2023-10-16" @default.
- W3199438302 title "On Lipschitz approximations in second order Sobolev spaces and the change of variables formula" @default.
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- W3199438302 doi "https://doi.org/10.1016/j.jmaa.2021.125659" @default.
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