Harmonic functions for a class of integro-differential operators
| dc.creator | Foondun, Mohammud | |
| dc.date | 2008-12-11 | |
| dc.date.accessioned | 2026-07-07T12:11:57Z | |
| dc.date.available | 2026-07-07T12:11:57Z | |
| dc.description | We consider the operator $\sL$ defined on $C^2(\bR^d)$ functions by \sL f(x)&=&{1/2}\sum_{i,j=1}^d a_{ij}(x)\frac{\partial^2f(x)}{\partial x_i\partial x_j}+\sum_{i=1}^d b_i(x)\frac{\partial f(x)}{\partial x_i} &+&\int_{\bR^d\backslash\{0\}}[f(x+h)-f(x)-1_{(|h|\leq1)}h\cdot \grad f(x)]n(x,h)dh. Under the assumption that the local part of the operator is uniformly elliptic and with suitable conditions on $n(x,h)$, we establish a Harnack inequality for functions that are nonnegative in $\bR^d$ and harmonic in a domain. We also show that the Harnack inequality can fail without suitable conditions on $n(x,h)$. A regularity theorem for those nonnegative harmonic functions is also proved | |
| dc.identifier | https://arxiv.org/abs/0812.2082 | |
| dc.identifier | http://arxiv.org/abs/0812.2082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210389 | |
| dc.subject | Probability | |
| dc.subject | 60J75 | |
| dc.title | Harmonic functions for a class of integro-differential operators | |
| dc.type | text |