| 실적년도 | 2011 년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Panki Kim, Renming Song,Zoran Vondracek |
| 학술지명 | Proceedings of the London Mathematical Society |
| 권(Vol.) | 104 |
| 호(No.) | 5 |
| 게재년월 | 년 월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
A subordinate Brownian motion is a Levy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is, where is the Laplace exponent of the subordinator. In this paper, we consider a large
class of subordinate Brownian motions without diffusion component and with comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes, sums of independent relativistic stable
processes, and much more. We give sharp two-sided estimates on the Green functions of these subordinate Brownian motions in any bounded k-fat open set D. When D is a bounded C1;1 open set, we establish an explicit form of the estimates in terms of the distance to the boundary. As a consequence of such
sharp Green function estimates, we obtain a boundary Harnack principle in C1;1 open sets with explicit rate of decay.
class of subordinate Brownian motions without diffusion component and with comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes, sums of independent relativistic stable
processes, and much more. We give sharp two-sided estimates on the Green functions of these subordinate Brownian motions in any bounded k-fat open set D. When D is a bounded C1;1 open set, we establish an explicit form of the estimates in terms of the distance to the boundary. As a consequence of such
sharp Green function estimates, we obtain a boundary Harnack principle in C1;1 open sets with explicit rate of decay.
