Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials
| dc.creator | Kim, Panki | |
| dc.creator | Song, Renming | |
| dc.date | 2006-05-30 | |
| dc.date | 2008-09-26 | |
| dc.date.accessioned | 2026-07-07T10:07:12Z | |
| dc.date.available | 2026-07-07T10:07:12Z | |
| dc.description | Recently, in [Preprint (2006)], we extended the concept of intrinsic ultracontractivity to nonsymmetric semigroups. In this paper, we study the intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and measure-valued potentials in bounded domains. Our process $Y$ is a diffusion process whose generator can be formally written as $L+μ\cdot\nabla-ν$ with Dirichlet boundary conditions, where $L$ is a uniformly elliptic second-order differential operator and $μ=(μ^1,...,μ^d)$ is such that each component $μ^i$, $i=1,...,d$, is a signed measure belonging to the Kato class $\mathbf{K}_{d,1}$ and $ν$ is a (nonnegative) measure belonging to the Kato class $\mathbf{K}_{d,2}$. We show that scale-invariant parabolic and elliptic Harnack inequalities are valid for $Y$. In this paper, we prove the parabolic boundary Harnack principle and the intrinsic ultracontractivity for the killed diffusion $Y^D$ with measure-valued drift and potential when $D$ is one of the following types of bounded domains: twisted Hölder domains of order $α\in(1/3,1]$, uniformly Hölder domains of order $α\in(0,2)$ and domains which can be locally represented as the region above the graph of a function. This extends the results in [J. Funct. Anal. 100 (1991) 181--206] and [Probab. Theory Related Fields 91 (1992) 405--443]. As a consequence of the intrinsic ultracontractivity, we get that the supremum of the expected conditional lifetimes of $Y^D$ is finite. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AOP381 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0605757 | |
| dc.identifier | http://arxiv.org/abs/math/0605757 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 5, 1904-1945 | |
| dc.identifier | doi:10.1214/07-AOP381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170549 | |
| dc.subject | Probability | |
| dc.subject | 47D07, 60J25 (Primary) 60J45 (Secondary) | |
| dc.title | Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials | |
| dc.type | text |