Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold

2025/05/08 by Ali, Hussein Cheikh, Robert, Frédéric · 1 citation
#35J60 #58J05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.05201

Abstract

We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical potential at the singular point. This condition is sharp as shown by the first author in [Cheikh-Ali, Pacific J. of Math. 2022].

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• Compactness for the Hardy-Sobolev equation on manifolds

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