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arXiv · 2105.03622

Fuglede's theorem in generalized Orlicz--Sobolev spaces

Jonne Juusti
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Abstract

In this paper, we show that Orlicz--Sobolev spaces $W^{1,ϕ}(Ω)$ can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that $C^1(Ω)$ functions are dense in $W^{1,ϕ}(Ω)$, and $ϕ(x,β) \geq 1$ for some $β> 0$ and almost every $x \in Ω$. The results are new even in the special cases of Orlicz and double phase growth.

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Jonne Juusti. 2021-05-08. Fuglede's theorem in generalized Orlicz--Sobolev spaces. https://arxiv.org/abs/2105.03622

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