Extension in generalized Orlicz--Sobolev spaces

2022/06/30 by Juusti, Jonne
#46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2206.15121

Abstract

We study the existence of an extension operator Λ\colon W^1,φ(Ω)→ W^1,ψ(ℝⁿ). We assume that φ∈ Φ_w(Ω) has generalized Orlicz growth, ψ∈ Φ_w(ℝⁿ) is an extension of φ, and that Ω⊂ℝⁿ is an (ε,δ)-domain. Special cases include the classical constant exponent case, the Orlicz case, the variable exponent case, and the double phase case.

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