Continuous Sobolev functions with singularity on arbitrary real-analytic sets
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909219064643584 |
|---|---|
| author | Pan, Yifei Zhang, Yuan |
| author_facet | Pan, Yifei Zhang, Yuan |
| contents | Near every point of a real-analytic set in $\mathbb R^n$, we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{loc}$ such that their weak derivatives have (removable) singularity precisely on that set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous Sobolev functions with singularity on arbitrary real-analytic sets Pan, Yifei Zhang, Yuan Analysis of PDEs Complex Variables Primary 32C07, Secondary 46E35, 14E15 Near every point of a real-analytic set in $\mathbb R^n$, we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{loc}$ such that their weak derivatives have (removable) singularity precisely on that set. |
| title | Continuous Sobolev functions with singularity on arbitrary real-analytic sets |
| topic | Analysis of PDEs Complex Variables Primary 32C07, Secondary 46E35, 14E15 |
| url | https://arxiv.org/abs/2406.04544 |