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- W1599514564 abstract "Let Ω be a bounded open subset of Rn with Lipschitz boundary, let n < σ < ∞ and let p : [1, n) belong to the Sobolev space W1,σ(Ω). Let W1,p(x)(Ω) be the Sobolev space modelled on the generalised Lebesgue space Lp(x)(Ω). We show that there is a constant c > 0 such that for all f ∈ W1,p(x)(Ω), where ∥·∥M,Ω is the norm on a certain space of Orlicz-Musielak type and ∥·∥1,p,Ω is the norm on W1,p(x)(Ω). This inequality reduces to the usual Sobolev inequality when supΩp < n. The paper extends earlier work of the authors ([ER]) in which it was assumed that p was Lipschitz-continuous." @default.
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- W1599514564 date "2002-12-01" @default.
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- W1599514564 doi "https://doi.org/10.1002/1522-2616(200212)246:1<53::aid-mana53>3.0.co;2-t" @default.
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