Let (M,g) be a non-locally conformally flat compact Riemannian manifold with dimension N≥7. We are interested in finding positive solutions to the linear perturbation of the Yamabe problem −Lgu+ϵu=uN+2N−2 in (M,g) where the first eigenvalue of the conformal laplacian −Lg is positive and ϵ is a small positive parameter. We prove that for any point ξ0∈M which is non-degenerate and non-vanishing minimum point of the Weyl's tensor and for any integer k there exists a family of solutions developing k peaks collapsing at ξ0 as ϵ goes to zero. In particular, ξ0 is a non-isolated blow-up point

Clustering phenomena for linear perturbation of the Yamabe equation / Pistoia, Angela; Vaira, Giusi. - (2019), pp. 311-331. - LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES.

Clustering phenomena for linear perturbation of the Yamabe equation.

Pistoia Angela;Vaira Giusi
2019

Abstract

Let (M,g) be a non-locally conformally flat compact Riemannian manifold with dimension N≥7. We are interested in finding positive solutions to the linear perturbation of the Yamabe problem −Lgu+ϵu=uN+2N−2 in (M,g) where the first eigenvalue of the conformal laplacian −Lg is positive and ϵ is a small positive parameter. We prove that for any point ξ0∈M which is non-degenerate and non-vanishing minimum point of the Weyl's tensor and for any integer k there exists a family of solutions developing k peaks collapsing at ξ0 as ϵ goes to zero. In particular, ξ0 is a non-isolated blow-up point
2019
Partial differential equations arising from physics and geometry.
978-1-108-43163-7
clustering phenomena, blow-up, yamabe problem
02 Pubblicazione su volume::02a Capitolo o Articolo
Clustering phenomena for linear perturbation of the Yamabe equation / Pistoia, Angela; Vaira, Giusi. - (2019), pp. 311-331. - LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1466968
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