Infinitely many solutions for a boundary Yamabe problem

We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of infinitely many non-radial positive solutions when the dimension is larger or equal to 5. This is the first result of existence of solutions in the case of negative prescribed scalar curvature problem in higher dimensions.

Publication Details

Journal
ArXiv.org
Published
2025-03-08
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Infinitely many solutions for a boundary Yamabe problem

ArXiv.org
Nonlinear Partial Differential Equations
article

Infinitely many solutions for a boundary Yamabe problem

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Abstract

We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of infinitely many non-radial positive solutions when the dimension is larger or equal to 5. This is the first result of existence of solutions in the case of negative prescribed scalar curvature problem in higher dimensions.

ArXiv.org
Openalex Percentile: Top 39%
Nonlinear Partial Differential Equations
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Infinitely many solutions for a boundary Yamabe problem · ArXiv.org (2025) | TGRS Research Map | TGRS