Regularity results for stable-like operators

被引：55
|
作者：
Bass, Richard F. [1 ]
机构：
[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2009年 / 257卷 / 08期
基金：
美国国家科学基金会;
关键词：
Semigroups; Holder; Stable-like; Non-local; SYMMETRIC JUMP-PROCESSES; HARNACK INEQUALITIES; HARMONIC-FUNCTIONS; MARKOV-PROCESSES; VARIABLE ORDER; KERNEL;
D O I：
10.1016/j.jfa.2009.05.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For alpha is an element of [1, 2) we consider operators of the form Lf (x) = (Rd)integral[f (x + h) - f (x)- 1((|h|<= 1))del f (x) . h]A(x, h)/|h|(d+a) dh and for alpha is an element of (0, 1) we consider the same operator but where the del f term is omitted. We prove, under appropriate conditions on A(x, h), that any solution u to Lu = f will be in C(alpha+beta) if f is an element of C(beta). (C) 2009 Elsevier Inc. All rights reserved.
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页码：2693 / 2722
页数：30
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