Browse

Heat kernel estimates for symmetric Markov processes in $C^{1,\eta}$ open sets

Cited 0 time in Web of Science Cited 0 time in Scopus
Authors
김경윤
Advisor
김판기
Major
자연과학대학 수리과학부
Issue Date
2015-08
Publisher
서울대학교 대학원
Keywords
Dirihlet formMarkov processheat kerneltransition densityGreen function
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 김판기.
Abstract
In this thesis, we establish sharp two-sided heat kernel estimates for a large class of symmetric Markov processes in $C^{1,\eta}$ open sets for all $t> 0$. The processes are symmetric pure jump Markov processes with jumping kernel intensity
$$\kappa(x, y)\psi(
x-y
)^{-1}
^{-d-\alpha}$$
where $\alpha\in(0,2)$, $\psi$ is an increasing function on $[ 0, \infty)$ with $\psi(r)=1$ on $01$ for $\beta\in[0, \infty]$. A symmetric function $\kappa(x, y)$ is bounded by two positive constants and $
\kappa(x, y)-\kappa(x,x)
\le c_5
^{\rho}$ for $
<1$ and $\rho>\alpha/2$. As a corollary of our main result, we estimates sharp two-sided Green function for this process in $C^{1,\eta}$ open sets.
Language
English
URI
https://hdl.handle.net/10371/121297
Files in This Item:
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse