Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911036629581824 |
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| author | Cazacu, Cristian Rugină, Teodor |
| author_facet | Cazacu, Cristian Rugină, Teodor |
| contents | In this paper, we prove generalizations to the L^p setting of the Hardy-Rellich inequalities on domains of R^N with singularity given by the distance function to the boundary. The inequalities we obtain are either sharp in bounded domains, where we provide concrete minimizing sequences, or give a new bound for the sharp constant, while also depending on the geometric properties of the domain and its boundary. We also give applications to the existence and non-existence of solutions for a singular problem using variational methods and a Pohozaev identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem Cazacu, Cristian Rugină, Teodor Analysis of PDEs In this paper, we prove generalizations to the L^p setting of the Hardy-Rellich inequalities on domains of R^N with singularity given by the distance function to the boundary. The inequalities we obtain are either sharp in bounded domains, where we provide concrete minimizing sequences, or give a new bound for the sharp constant, while also depending on the geometric properties of the domain and its boundary. We also give applications to the existence and non-existence of solutions for a singular problem using variational methods and a Pohozaev identity. |
| title | Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.02551 |