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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
