In:
Canadian Journal of Mathematics, Canadian Mathematical Society, Vol. 38, No. 5 ( 1986-10-01), p. 1181-1198
Abstract:
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 W Kp (∧) and u/d k ∊ L p (∧), 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
Type of Medium:
Online Resource
ISSN:
0008-414X
,
1496-4279
DOI:
10.4153/CJM-1986-059-4
Language:
English
Publisher:
Canadian Mathematical Society
Publication Date:
1986
detail.hit.zdb_id:
1467410-5
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