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- W2093742437 abstract "Let Ω ⊂ ℝ N , N ≥ 2, be a smooth bounded domain. It is shown that: (a) if [Formula: see text] and ess inf x ∈ y p(x) > 1, then the generalized Lebesgue space (L p (·) (Ω), ‖·‖ p(·) ) is smooth; (b) if [Formula: see text] and p(x) > 1, [Formula: see text], then the generalized Sobolev space [Formula: see text] is smooth. In both situations, the formulae for the Gâteaux gradient of the norm corresponding to each of the above spaces are given; (c) if [Formula: see text] and p(x) ≥ 2, [Formula: see text], then [Formula: see text] is uniformly convex and smooth." @default.
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- W2093742437 date "2009-10-01" @default.
- W2093742437 modified "2023-10-18" @default.
- W2093742437 title "GEOMETRY OF SOBOLEV SPACES WITH VARIABLE EXPONENT AND A GENERALIZATION OF THE p-LAPLACIAN" @default.
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- W2093742437 doi "https://doi.org/10.1142/s0219530509001451" @default.
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