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

被引：86

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

页码：1249 / 1259

页数：11

共 50 条

[1] Intrinsic Holder Continuity of Harmonic Functions
Hansen, Wolfhard
POTENTIAL ANALYSIS, 2017, 47 (01) : 1 - 12
[2] Holder continuity of p(x)-harmonic functions
Alkhutov, YA
SBORNIK MATHEMATICS, 2005, 196 (1-2) : 147 - 171
[3] HOLDER CONTINUITY OF DEGENERATE p-HARMONIC FUNCTIONS
Giannetti, Flavia
di Napoli, Antonia Passarelli
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2014, 39 (02) : 567 - 577
[4] HOLDER CONTINUITY OF MULTIPLE VALUED HARMONIC-FUNCTIONS
CAFFARELLI, LA
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1976, 25 (01) : 79 - 84
[5] Holder Continuity of Generalized Harmonic Functions in the Unit Disc
Khalfallah, Adel
Mhamdi, Mohamed
COMPLEX ANALYSIS AND OPERATOR THEORY, 2022, 16 (07)
[6] Weighted holder continuity of hyperbolic harmonic Bloch functions
Ren, GB
Kähler, U
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2002, 21 (03): : 599 - 610
[7] Spherical convolution operators in spaces of variable Holder order
Vakulov, B. G.
MATHEMATICAL NOTES, 2006, 80 (5-6) : 645 - 657
[8] A condition equivalent to the Holder continuity of harmonic functions on unbounded Lipschitz domains
Markovic, Marijan
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2025,
[9] Holder Continuity and Harnack's Inequality for p(x)-Harmonic Functions
Alkhutov, Yu. A.
Surnachev, M. D.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2020, 308 (01) : 1 - 21
[10] THE DERIVATION OF HARMONIC-FUNCTIONS WITH RESPECT TO A VARIABLE FIELD
DETRAZ, J
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 96 (04) : 614 - 616

← 1 2 3 4 5 →