On divergence operators: Free space and vanishing charges
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910059280203776 |
|---|---|
| author | De Pauw, Thierry |
| author_facet | De Pauw, Thierry |
| contents | We use localized topologies to prove existence and optimal regularity results for the divergence equation $\mathrm{div} (v) = F$ in critical cases $v \in L_1(Ω;\mathbb{R}^m)$ or $v \in C_0(Ω;\mathbb{R}^m)$, i.e. we characterize those $F$ for which a solution $v$ exists whose norm is bounded by an appropriate norm of $F$. We assume $Ω$ satisfies a Poincaré inequality or an extension property. We apply the general theory to give examples of admissible $F$ in each case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18441 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On divergence operators: Free space and vanishing charges De Pauw, Thierry Analysis of PDEs Functional Analysis 35F15, 35Q35, 42B35, 35F05, 46F05, 35D30 We use localized topologies to prove existence and optimal regularity results for the divergence equation $\mathrm{div} (v) = F$ in critical cases $v \in L_1(Ω;\mathbb{R}^m)$ or $v \in C_0(Ω;\mathbb{R}^m)$, i.e. we characterize those $F$ for which a solution $v$ exists whose norm is bounded by an appropriate norm of $F$. We assume $Ω$ satisfies a Poincaré inequality or an extension property. We apply the general theory to give examples of admissible $F$ in each case. |
| title | On divergence operators: Free space and vanishing charges |
| topic | Analysis of PDEs Functional Analysis 35F15, 35Q35, 42B35, 35F05, 46F05, 35D30 |
| url | https://arxiv.org/abs/2603.18441 |