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- W3204259060 abstract "Following Mal'y's definition of absolutely continuous functions of several variables, we consider $Q$-absolutely continuous mappings $fcolon Xto V$ between a doubling metric measure space $X$ and a Banach space $V$. The relation between these mappings and Sobolev mappings $fin N^{1,p}(X;V)$ for $pge Q$ is investigated. In particular, a locally $Q$-absolutely continuous mapping on an Ahlfors $Q$-regular space is a continuous mapping in $N^{1,Q}_{rm{loc}}(X;V)$, as well as differentiable almost everywhere in terms of Cheeger derivatives provided $V$ satisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mapping $fin N^{1,Q}_{rm{loc}}(X;V)$ is generally not locally $Q$-absolutely continuous, this implication holds if $f$ is further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are also $Q$-absolutely continuous." @default.
- W3204259060 created "2021-10-11" @default.
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- W3204259060 date "2021-09-28" @default.
- W3204259060 modified "2023-09-27" @default.
- W3204259060 title "Absolutely continuous mappings on doubling metric measure spaces" @default.
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- W3204259060 doi "https://doi.org/10.48550/arxiv.2109.13615" @default.
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