A nonexistence result for Yamabe type problems on thin annuli
نویسندگان
چکیده
منابع مشابه
Energy and Morse index of solutions of Yamabe type problems on thin annuli
We consider the Yamabe type family of problems (Pε): −1uε = u (n+2)/(n−2) ε , uε > 0 in Aε , uε = 0 on ∂Aε , where Aε is an annulus-shaped domain of Rn, n ≥ 3, which becomes thinner as ε→ 0. We show that for every solution uε , the energy ∫ Aε |∇uε| 2 as well as the Morse index tend to infinity as ε → 0. This is proved through a fine blow up analysis of appropriate scalings of solutions whose l...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2002
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(02)00101-4