Ellipticity and Ergodicity
| dc.creator | Robinson, Derek W. | |
| dc.creator | Sikora, Adam | |
| dc.date | 2008-02-20 | |
| dc.date | 2009-02-25 | |
| dc.date.accessioned | 2026-07-07T12:46:01Z | |
| dc.date.available | 2026-07-07T12:46:01Z | |
| dc.description | Let $S=\{S_t\}_{t\geq0}$ be the submarkovian semigroup on $L_2(\Ri^d)$ generated by a self-adjoint, second-order, divergence-form, elliptic operator $H$ with Lipschitz continuous coefficients $c_{ij}$. Further let $Ω$ be an open subset of $\Ri^d$. Under the assumption that $C_c^\infty(\Ri^d)$ is a core for $H$ we prove that $S$ leaves $L_2(Ω)$ invariant if, and only if, it is invariant under the flows generated by the vector fields $Y_i=\sum^d_{j=1}c_{ij}\partial_j$. | |
| dc.description | 8 pages--Replacement, with corrections, of an earlier version | |
| dc.identifier | https://arxiv.org/abs/0802.2743 | |
| dc.identifier | http://arxiv.org/abs/0802.2743 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221241 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J70, 35Hxx, 35F05, 31C15 | |
| dc.title | Ellipticity and Ergodicity | |
| dc.type | text |