Density of  C   ∞ (Ω) in W   1, p  ( x  ) (Ω) with discontinuous exponent  p  ( x  ) | Zendy

Fan Xianling | Zendy; Wang Suyun | Zendy; Zhao Dun | Zendy

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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)

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