Fuglede's theorem in generalized Orlicz--Sobolev spaces

2021/05/08 by Juusti, Jonne
#46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.03622

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 C¹(Ω) functions are dense in W^1,ϕ(Ω), and ϕ(x,β) ≥ 1 for some β> 0 and almost every x ∈ Ω. The results are new even in the special cases of Orlicz and double phase growth.

Related

• Density of compactly supported smooth functions C_C^∞(ℝ^d) in Musielak-Orlicz-Sobolev spaces W^1,Φ(Ω)
• Extension in generalized Orlicz--Sobolev spaces
• A density result on Orlicz-Sobolev spaces in the plane
• Density of smooth functions in Musielak-Orlicz spaces
• Sobolev embeddings in Musielak-Orlicz space