L1 Compactness of Bounded BV Sets
| dc.creator | Fleischer, Isidore | |
| dc.date | 2002-12-15 | |
| dc.date.accessioned | 2026-07-07T04:53:47Z | |
| dc.date.available | 2026-07-07T04:53:47Z | |
| dc.description | Functions, uniformly bounded in $BV$ norm in some bounded open set $U$ in $R^n$, are compact in $L_1(U)$. This result is known when $U$ has Lipschitz boundary [EG Th. 4 p. 176], [G 1.19 Th. p. 17], [Z 5.34 Cor. p. 227]; the proof for general $U$ here, after identifying the operator theoretic definition of bounded $BV$ norm with that of the Tonelli variation, appeals to the standard compactness criterion in $L_1$ [DS 21 TH. p. 301] [Y, p. 275] (For completeness, these two auxiliary results are also presented). | |
| dc.description | 3 pages | |
| dc.identifier | https://arxiv.org/abs/math/0212198 | |
| dc.identifier | http://arxiv.org/abs/math/0212198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65992 | |
| dc.subject | Functional Analysis | |
| dc.title | L1 Compactness of Bounded BV Sets | |
| dc.type | text |