Desingularization of Clifford Torus and Nonradial Solutions to Yamabe Problem with Maximal Rank

2017/12/01 by María Medina, Monica Musso, Medina, María +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1712.00326

openalex publication_date 2017/12/01 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts-Kenig-Merle nodal nonradial solutions to the critical Yamabe problem -Δu=(n(n-2))/(4)|u|^(4)/(n-2)u, u∈ D^1,2(Rⁿ). The case n=4 is the first example in the literature of a solution with \em maximal rank \mathcal N=2n+1+(n(n-1))/(2).

Citations

• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

Related

• Nondegeneracy of Nonradial Nodal Solutions to Yamabe Problem
• Doubling nodal solutions to the Yamabe equation in ℝⁿ with maximal rank
• Multiplicity of nodal solutions to the Yamabe problem
• Non-radial solutions of the problem -Δu = |u|^4/(n-2)u in Rⁿ, n≥3
• Concentration on minimal submanifolds for a Yamabe type problem