We consider a small perturbation of the geometric Paneitz equation Delta(2)(g)u - div(g)((A(g) + epsilon B)(del u)(#)) + N - 4/2 Q(g)u = vertical bar u vertical bar(2#-2)u, on a smooth, compact Riemannian manifold of dimension N >= 9. Here A(g),B are smooth and symmetric (2,0)-tensor fields and Q(g) is the Q-curvature of g. Under suitable conditions, we construct solutions that blow up at one point of the manifold. This implies immediately that the equation is not stable.

On the Stability for Paneitz-Type Equations / Pistoia, Angela; Vaira, Giusi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - (2013), pp. 3133-3158. [10.1093/imrn/rns133]

On the Stability for Paneitz-Type Equations

PISTOIA, Angela;VAIRA, GIUSI
2013

Abstract

We consider a small perturbation of the geometric Paneitz equation Delta(2)(g)u - div(g)((A(g) + epsilon B)(del u)(#)) + N - 4/2 Q(g)u = vertical bar u vertical bar(2#-2)u, on a smooth, compact Riemannian manifold of dimension N >= 9. Here A(g),B are smooth and symmetric (2,0)-tensor fields and Q(g) is the Q-curvature of g. Under suitable conditions, we construct solutions that blow up at one point of the manifold. This implies immediately that the equation is not stable.
2013
01 Pubblicazione su rivista::01a Articolo in rivista
On the Stability for Paneitz-Type Equations / Pistoia, Angela; Vaira, Giusi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - (2013), pp. 3133-3158. [10.1093/imrn/rns133]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/485207
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