<Emphasis Type="Italic">BV</Emphasis> functions and parabolic initial boundary value problems on domains |
| |
Authors: | Luciana Angiuli Jr" target="_blank">Michele MirandaJr Diego Pallara Fabio Paronetto |
| |
Institution: | (1) Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, P. O. Box 193, 73100 Lecce, Italy;(2) Dipartimento di Matematica, Università di Ferrara, Via Machiavelli, 35, 44100 Ferrara, Italy |
| |
Abstract: | Given a uniformly elliptic second order operator on a possibly unbounded domain , let (T(t))
t≥0 be the semigroup generated by in L
1(Ω), under homogeneous co-normal boundary conditions on ∂Ω. We show that the limit as t → 0 of the L
1-norm of the spatial gradient D
x
T(t)u
0 tends to the total variation of the initial datum u
0, and in particular is finite if and only if u
0 belongs to BV(Ω). This result is true also for weighted BV spaces. A further characterization of BV functions in terms of the short-time behaviour of (T(t))
t≥0 is also given.
|
| |
Keywords: | Linear parabolic equations BV functions Semigroup theory |
本文献已被 SpringerLink 等数据库收录! |
|