On solutions to Hardy-Sobolev equations on Riemannian manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917176204591104 |
|---|---|
| author | Henry, Guillermo Petean, Jimmy |
| author_facet | Henry, Guillermo Petean, Jimmy |
| contents | Let $(M,g)$ be a closed Riemannian manifold of dimension at least $3$. Let $S$ be the union of the focal submanifolds of an isoparametric function on $(M,g)$. In this article we address the existence of solutions of the Hardy-Sobolev type equation $Δ_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s}$, where $d_{S}(x)$ is the distance from $x$ to $S$ and $q>2$. In particular, we will prove the existence of infinite sign-changing solutions to the equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On solutions to Hardy-Sobolev equations on Riemannian manifolds Henry, Guillermo Petean, Jimmy Analysis of PDEs Differential Geometry Let $(M,g)$ be a closed Riemannian manifold of dimension at least $3$. Let $S$ be the union of the focal submanifolds of an isoparametric function on $(M,g)$. In this article we address the existence of solutions of the Hardy-Sobolev type equation $Δ_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s}$, where $d_{S}(x)$ is the distance from $x$ to $S$ and $q>2$. In particular, we will prove the existence of infinite sign-changing solutions to the equation. |
| title | On solutions to Hardy-Sobolev equations on Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2506.20089 |