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
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.
