A biharmonic problem with constraint involving critical Sobolev exponent
M. Guedda, Rejeb Hadiji, Colette Picard · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2001
We are concerned with the following minimization problems, where Ω ⊂ RN, N > 4, is a smooth bounded domain, qc = 2N/(N − 4), ϕ ∈ C(Ω) ∩ Lqc(Ω) and . We show that, for ϕ ≢ 0, each infimum is achieved. Under suitable conditions on ϕ, we establish the following gap phenomenon, for q ≤ qc. Moreover, we study the limit behaviour of the minimizers, as q goes to qc, in the case ϕ ∈ H(Ω).