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Density of C ∞ (Ω) in W 1, p ( x ) (Ω) with discontinuous exponent p ( x )
Author(s) -
Fan Xianling,
Wang Suyun,
Zhao Dun
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310351
Subject(s) - exponent , mathematics , lipschitz continuity , combinatorics , mathematical physics , mathematical analysis , philosophy , linguistics
In this paper, we present a sufficient condition for the density of C ∞ (Ω) in W 1, p ( x ) (Ω) with p ( x ) being discontinuous. Roughly speaking, we can get the density under the following assumptions: 1) Ω can be divided into some open pieces Ω i such that p ( x ) is “fine”on each Ω i , for example, p ( x ) satisfies the Dini–Lipschitz condition on each Ω i . 2) The corresponding pieces “get along with each other regularly ”. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)