Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P( )(Ω), where p(.) : Ω → [1, ∞[ is a variable exponent. This inequality is...Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P( )(Ω), where p(.) : Ω → [1, ∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space ;D(Ω) in the space {v ∈ Wl,P( )(Ω); tr v = 0 on δΩ}. Two applications are also discussed.展开更多
基金supported partly by the China Postdoctoral Science Foundation(2013M541899)the Natural Science Foundation of Shandong Province of China(ZR2013AQ021)the Independent Innovation Foundation of Shandong University(2012GN016)
基金Supported by the National Natural Science Foundation of China(10661006)the Support Program of New Century Guangxi Ten-hundred-thousand Talents Project(2005214)the Guangxi Science Foundation(0728212)
文摘Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P( )(Ω), where p(.) : Ω → [1, ∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space ;D(Ω) in the space {v ∈ Wl,P( )(Ω); tr v = 0 on δΩ}. Two applications are also discussed.