Global hypoellipticity for perturbations of complex vector fields on the torus
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910031926001664 |
|---|---|
| author | Bartmeyer, Maria V. da Silva, Paulo L. Dattori Gonzalez, Rafael B. |
| author_facet | Bartmeyer, Maria V. da Silva, Paulo L. Dattori Gonzalez, Rafael B. |
| contents | We apply Krönecker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present situations in which this set is a discrete enumerable (hence, meager) subset of the real line, and we also show that this set may be a dense $\mathcal{G}_δ$ subset of the complex numbers (hence, nonmeager), which produces a contrast to a known result stating that this set has null Lebesgue measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity for perturbations of complex vector fields on the torus Bartmeyer, Maria V. da Silva, Paulo L. Dattori Gonzalez, Rafael B. Analysis of PDEs Primary 35F05, 35H10. Secondary 35B10, 35B65, 42B05 We apply Krönecker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present situations in which this set is a discrete enumerable (hence, meager) subset of the real line, and we also show that this set may be a dense $\mathcal{G}_δ$ subset of the complex numbers (hence, nonmeager), which produces a contrast to a known result stating that this set has null Lebesgue measure. |
| title | Global hypoellipticity for perturbations of complex vector fields on the torus |
| topic | Analysis of PDEs Primary 35F05, 35H10. Secondary 35B10, 35B65, 42B05 |
| url | https://arxiv.org/abs/2602.21159 |