Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908758266871808 |
|---|---|
| author | Farkas, Csaba Kajántó, Sándor |
| author_facet | Farkas, Csaba Kajántó, Sándor |
| contents | In this paper we establish higher-order Sobolev and Rellich-type inequalities on non-compact Riemannian manifolds supporting an isoperimetric inequality. We highlight two notable settings: manifolds with non-negative Ricci curvature and having Euclidean volume growth (supporting Brendle's isoperimetric inequality) and manifolds with non-positive sectional curvature (satisfying the Cartan-Hadamard conjecture or supporting Croke's isoperimetric inequality). Our proofs rely on various symmetrization techniques, the key ingredient is an iterated Talenti's comparison principle. The non-iterated version is analogous to the main result of Chen and Li [J. Geom. Anal., 2023]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle Farkas, Csaba Kajántó, Sándor Analysis of PDEs In this paper we establish higher-order Sobolev and Rellich-type inequalities on non-compact Riemannian manifolds supporting an isoperimetric inequality. We highlight two notable settings: manifolds with non-negative Ricci curvature and having Euclidean volume growth (supporting Brendle's isoperimetric inequality) and manifolds with non-positive sectional curvature (satisfying the Cartan-Hadamard conjecture or supporting Croke's isoperimetric inequality). Our proofs rely on various symmetrization techniques, the key ingredient is an iterated Talenti's comparison principle. The non-iterated version is analogous to the main result of Chen and Li [J. Geom. Anal., 2023]. |
| title | Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.19198 |