Nodal cluster solutions for the Brezis-Nirenberg problem in dimensions N≥ 7

2023/11/29 by Monica Musso, Musso, Monica, Serena Rocci +3 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2311.17436

Abstract

We show that the classical Brezis-Nirenberg problem Δu + |u|^{4 \over N-2} u + ε u = 0 , \mbox in Ω, u= 0 , \mbox on ∂ Ω admits nodal solutions clustering around a point on the boundary of Ω as ε → 0, for smooth bounded domains Ω⊂ ℝ^N in dimensions N≥ 7.

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