A biharmonic problem with constraint involving critical Sobolev exponent
Published online by Cambridge University Press: 12 July 2007
Abstract
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).
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1113 - 1132
- Copyright
- Copyright © Royal Society of Edinburgh 2001
- 1
- Cited by