Nonautonomous Kolmogorov parabolic equations with unbounded coefficients
| dc.creator | Kunze, M. | |
| dc.creator | Lorenzi, L. | |
| dc.creator | Lunardi, A. | |
| dc.date | 2008-04-09 | |
| dc.date.accessioned | 2026-07-07T09:31:17Z | |
| dc.date.available | 2026-07-07T09:31:17Z | |
| dc.description | We study a class of elliptic operators $A$ with unbounded coefficients defined in $I\times\CR^d$ for some unbounded interval $I\subset\CR$. We prove that, for any $s\in I$, the Cauchy problem $u(s,\cdot)=f\in C_b(\CR^d)$ for the parabolic equation $D_tu=Au$ admits a unique bounded classical solution $u$. This allows to associate an evolution family $\{G(t,s)\}$ with $A$, in a natural way. We study the main properties of this evolution family and prove gradient estimates for the function $G(t,s)f$. Under suitable assumptions, we show that there exists an evolution system of measures for $\{G(t,s)\}$ and we study the first properties of the extension of $G(t,s)$ to the $L^p$-spaces with respect to such measures. | |
| dc.description | To appear on Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/0804.1430 | |
| dc.identifier | http://arxiv.org/abs/0804.1430 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158406 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 47D06, 47F05, 35B65 | |
| dc.title | Nonautonomous Kolmogorov parabolic equations with unbounded coefficients | |
| dc.type | text |