A density result on Orlicz-Sobolev spaces in the plane

Ortiz, Walter A.; Rajala, Tapio

doi:10.1016/j.jmaa.2021.125329

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“…Special cases of Orlicz growth include the classical constant exponent case ϕ(x, t) = t p , the Orlicz case ϕ(x, t) = ϕ(t), the variable exponent case ϕ(x, t) = t p(x) , and the double phase case ϕ(x, t) = t p +a(x)t q . Generalized Orlicz and Orlicz-Sobolev spaces on R n have recently been studied in [1,8,11,12] for example.…”

Section: Introductionmentioning

confidence: 99%

Fuglede’s theorem in generalized Orlicz–Sobolev spaces

Juusti

2021

Collect. Math.

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In this paper, we show that Orlicz–Sobolev spaces $$W^{1,\varphi }(\varOmega )$$ 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 $$C^1(\varOmega )$$ C 1 ( Ω ) functions are dense in $$W^{1,\varphi }(\varOmega )$$ W 1 , φ ( Ω ) , and $$\varphi (x,\beta ) \ge 1$$ φ ( x , β ) ≥ 1 for some $$\beta > 0$$ β > 0 and almost every $$x \in \varOmega $$ x ∈ Ω . The results are new even in the special cases of Orlicz and double phase growth.

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Section: Introductionmentioning

confidence: 99%