Some non-stability results for geometric Paneitz–Branson type equations

Laurent Bakri 1 Jean-Baptiste Casteras 2
2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : Let (M, g) be a compact riemannian manifold of dimension n ≥ 5. We consider two Paneitz-Branson type equations with general coefficients ∆ 2 g u − div g (A g du) + hu = |u| 2 * −2−ε u on M, (E1) and ∆ 2 g u − div g ((A g + εB g)du) + hu = |u| 2 * −2 u on M, (E2) where A g and B g are smooth symmetric (2, 0)-tensors, h ∈ C ∞ (M), 2 * = 2n n − 4 and ε is a small positive parameter. Under suitable assumptions , we construct solutions u ε to (??) and (??) which blow up at one point of the manifold when ε tends to 0. In particular, we extend the result of Deng and Pistoia 2011 (to the case where A g is the one defined in the Paneitz operator) and the result of Pistoia and Vaira 2013 (to the case n = 8 and (M, g) locally conformally flat).
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Submitted on : Monday, January 14, 2019 - 9:36:09 PM
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Laurent Bakri, Jean-Baptiste Casteras. Some non-stability results for geometric Paneitz–Branson type equations. Nonlinearity, IOP Publishing, 2015, 28 (9), pp.3337-3363. ⟨hal-01981194⟩

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