Holder continuity of harmonic functions with respect to operators of variable order

被引：87
作者：
Bass, RF [1 ]
Kassmann, M
机构：
[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
[2] Univ Bonn, Inst Angew Math, D-5300 Bonn, Germany
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 30卷 / 08期
基金：
美国国家科学基金会;
关键词：
continuity estimates; harmonic functions; Markov jump processes; Martingale problem; regularity;
D O I：
10.1080/03605300500257677
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of integrodifferential operators and their corresponding harmonic functions. Under mild assumptions on the family of jump measures we prove a priori estimates and establish Holder continuity of bounded functions that are harmonic in a domain.
引用
收藏
页码：1249 / 1259
页数：11
相关论文
共 32 条
[1]   UNIQUENESS IN LAW FOR PURE JUMP MARKOV-PROCESSES [J].
BASS, RF .
PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (02) :271-287
[2]   Harnack inequalities for non-local operators of variable order [J].
Bass, RF ;
Kassmann, M .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (02) :837-850
[3]   Harnack inequalities for jump processes [J].
Bass, RF ;
Levin, DA .
POTENTIAL ANALYSIS, 2002, 17 (04) :375-388
[4]   Transition probabilities for symmetric jump processes [J].
Bass, RF ;
Levin, DA .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (07) :2933-2953
[5]  
Basset Rene., 1904, Patrologia Orientalis, V1, P1
[6]   Heat kernel estimates for stable-like processes on d-sets [J].
Chen, ZQ ;
Kumagai, T .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 108 (01) :27-62
[7]  
Giorgi E. De., 1957, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Math. Nat., V3, P25
[8]  
Hoh W, 2000, REV MAT IBEROAM, V16, P219
[9]   THE MARTINGALE PROBLEM FOR A CLASS OF PSEUDODIFFERENTIAL-OPERATORS [J].
HOH, W .
MATHEMATISCHE ANNALEN, 1994, 300 (01) :121-147
[10]  
Hoh W., 1995, STOCH STOCH REP, V55, P225
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