Geodesic
Distance Functions and Orlicz-Sobolev Spaces
Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1181-1198

Voir la notice de l'article provenant de la source Cambridge University Press

Let ∧ be a bounded, non-empty, open subset of R n and given any x in R n , let let k ∊ N and suppose that p ∞ (1, ∞). It is known (c.f. e.g. [4]) that if u belongs to the Sobolev space WKp(∧) and u/dk ∊ Lp(∧), then . Further results in this direction are given in [5] and [9]. Moreover, if m is the mean distance function in the sense of [2], then it turns out that Under appropriate smoothness conditions on the boundary of ∧, m and d are equivalent, and thus may in this case be characterized as the subspace of W 1,2(∧) consisting of all functions u ∊ W 1,2(∧) such that u/d ∊ L 2(∧). Further results in this direction are given in [5] and [9]. Moreover, if m is the mean distance function in the sense of [2], then it turns out that 
Edmunds, D. E.; Edmunds, R. M. Distance Functions and Orlicz-Sobolev Spaces. Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1181-1198. doi: 10.4153/CJM-1986-059-4
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