On Yamabe type problems on Riemannian manifolds with boundary

2015/06/30 by Ghimenti, Marco, Micheletti, Anna Maria, Pistoia, Angela · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.09105

Abstract

Let (M,g) be a n-dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \ -Δ_gu+au=0 · amp; on M
∂_νu+(n-2)/(2)bu= u^n\over n-2±ε · amp; on ∂ M. where a∈ C¹(M), b∈ C¹(∂ M), ν is the outward pointing unit normal to ∂ M and ε is a small positive parameter. We build solutions which blow-up at a point of the boundary as ε goes to zero. The blowing-up behavior is ruled by the function b-H_g , where H_g is the boundary mean curvature.

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