Elliptic variational problems with critical exponent
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Veronica Felli Elliptic variational problems with critical exponent Thesis submitted for the degree of Doctor Philosophiae Academic year 2002-2003 Supervisor: Prof. Antonio Ambrosetti
46 4 Caffarelli-Kohn-Nirenberg type
5 Blow-up analysis for Caffarelli-K
5.1 Regularity for equations of Caf
There holds ∫ 1 (∇K · x) up p
then where 5.2 A Pohozaev-type iden
5.3 Local blow-up analysis 69 Defin
5.3 Local blow-up analysis 71 To pr
5.3 Local blow-up analysis 73 A dir
−2(1+a−b)(N−2−2a) We can ch
−div (|x| −2a ∇(u − AG a ))
∫ − |x| −2a ∂ ( ) ui (x i )
5.3 Local blow-up analysis 81 ξ i
u(q ∗ )/ω a (q ∗ )dist(q ∗ ,
5.4 A-priori estimates 85 Propositi
5.4 A-priori estimates 87 Proof. Su
∫ B ri (x i) 5.4 A-priori estimat
5.5 Leray-Schauder degree 91 lim di
hence in view of (5.119) 5.5 Leray-
5.5 Leray-Schauder degree 95 Hence
98 6 About an equation involving Ha
100 6 About an equation involving H
102 6 About an equation involving H
104 6 About an equation involving H
106 6 About an equation involving H
108 6 About an equation involving H
110 6 About an equation involving H
112 6 About an equation involving H
114 6 About an equation involving H
116 6 About an equation involving H
118 6 About an equation involving H
120 6 About an equation involving H
7 S 2 -type surfaces with prescribe
7.2 Analytical formulation 125 n v
7.3 Existence of H-bubbles via pert
142 References 17. A. Ambrosetti, A
144 References 62. S. Hildebrandt,
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Magazine: Elliptic variational problems with critical exponent