Weconsidertheproblemofprescribingthescalarandboundarymeancurva- tures via conformal deformation of the metric on a n− dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature K and boundary mean cur- 2 vature H of arbitrary sign which are non-constant and Dn = n(n − 1)H |K| −1 > 1 at some point of the boundary. It is known that this problem admits a positive mountain pass solution if n = 3, while no existence results are known for n ≥ 4. We will consider a perturbation of the geometric problem and show the existence of a positive solution which blows-up at a boundary point which is critical for both prescribed curvatures.
POSITIVE BLOW-UP SOLUTIONS FOR A LINEARLY PERTURBED BOUNDARY YAMABE PROBLEM
GIUSI VAIRA
In corso di stampa
Abstract
Weconsidertheproblemofprescribingthescalarandboundarymeancurva- tures via conformal deformation of the metric on a n− dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature K and boundary mean cur- 2 vature H of arbitrary sign which are non-constant and Dn = n(n − 1)H |K| −1 > 1 at some point of the boundary. It is known that this problem admits a positive mountain pass solution if n = 3, while no existence results are known for n ≥ 4. We will consider a perturbation of the geometric problem and show the existence of a positive solution which blows-up at a boundary point which is critical for both prescribed curvatures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
