The Dirichlet problem for a family of totally degenerate differential operators
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908495694004224 |
|---|---|
| author | Manfredini, Maria Piccinini, Mirco Polidoro, Sergio |
| author_facet | Manfredini, Maria Piccinini, Mirco Polidoro, Sergio |
| contents | In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense of Bony, differential operators. We also state and prove a Wiener-type criterium and an exterior cone condition for the regularity of a boundary point. Our results apply to a wide family of strongly degenerate operators that includes the following example $\mathcal{L} = t^2Δ_x + \langle x, \nabla_y \rangle -\partial_t$, for $(x,y,t) \in \mathbb{R}^N \times \mathbb{R}^{N} \times \mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_12048 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Dirichlet problem for a family of totally degenerate differential operators Manfredini, Maria Piccinini, Mirco Polidoro, Sergio Analysis of PDEs 35K70, 35B65, 35K20, 31B20, 31B25, 31D05 In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense of Bony, differential operators. We also state and prove a Wiener-type criterium and an exterior cone condition for the regularity of a boundary point. Our results apply to a wide family of strongly degenerate operators that includes the following example $\mathcal{L} = t^2Δ_x + \langle x, \nabla_y \rangle -\partial_t$, for $(x,y,t) \in \mathbb{R}^N \times \mathbb{R}^{N} \times \mathbb{R}$. |
| title | The Dirichlet problem for a family of totally degenerate differential operators |
| topic | Analysis of PDEs 35K70, 35B65, 35K20, 31B20, 31B25, 31D05 |
| url | https://arxiv.org/abs/2106.12048 |