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17 p, 209.1 KB Sobolev inequalities with variable exponent attaining the values 1 and n / Harjulehto, Petteri (University of Helsinki. Department of Mathematics and Statistics) ; Hästö, Peter (University of Oulu. Department of Mathematical Sciences)
We study Sobolev embeddings in the Sobolev space W1,p(·) (Ω) with variable exponent satisfying 1 6 p(x) 6 n. Since the exponent is allowed to reach the values 1 and n, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of L∞ at the upper end.
2008 - 10.5565/PUBLMAT_52208_05
Publicacions matemàtiques, V. 52 n. 2 (2008) p. 347-363  

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