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arXiv · 2505.05201

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

Hussein Cheikh Ali·Frédéric Robert
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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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Hussein Cheikh Ali, Frédéric Robert. 2025-05-08. Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold. https://arxiv.org/abs/2505.05201

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