A global compactness result for a mixed boundary value problem in half cylinder. (April 2016) - Fang, Fei; Xu, Jiankai
Abstract: Let Ω be a bounded smooth domain in R N with N ≥ 2, C = Ω × ( 0, ∞ ) and u n ⊂ H 0, L 1 ( C ) be a (P.S.) sequence of the functional I λ ( u ) = 1 2 ∫ C ∣ ∇ u ∣ 2 d x d y − λ 2 ∫ Ω × 0 ∣ u ∣ 2 d x − N − 1 2 N ∫ Ω × 0 ∣ u ∣ 2 N N − 1 d x, λ ∈ R . We study the limit behaviour of u n and obtain a global compactness result.