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A biharmonic problem with constraint involving critical Sobolev exponent

Published online by Cambridge University Press:  12 July 2007

M. Guedda ,
R. Hadiji  and
C. Picard
M. Guedda
Affiliation:
Lamfa, CNRS UPRES-A 6119, Université de Picardie Jules Verne, Faculté de Mathématiques et d'Informatique, 33 rue Saint-Leu 80039 Amiens, France
R. Hadiji
Affiliation:
Lamfa, CNRS UPRES-A 6119, Université de Picardie Jules Verne, Faculté de Mathématiques et d'Informatique, 33 rue Saint-Leu 80039 Amiens, France
C. Picard
Affiliation:
Lamfa, CNRS UPRES-A 6119, Université de Picardie Jules Verne, Faculté de Mathématiques et d'Informatique, 33 rue Saint-Leu 80039 Amiens, France
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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

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