Harmonic Functions for a Class of Integro-differential Operators

被引：13

作者：

Foondun, Mohammud ^{[1
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

POTENTIAL ANALYSIS | 2009年 / 31卷 / 01期

关键词：

Harnack inequality; Harmonic functions; Jump processes; Integro-differential operators; DIFFERENTIAL EQUATIONS; HARNACK INEQUALITIES; HOLDER CONTINUITY; VARIABLE ORDER; JUMP-PROCESSES;

D O I：

10.1007/s11118-009-9121-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the operator L defined on C(2)(R(d)) functions by [GRAPHICS] Under the assumption that the local part of the operator is uniformly elliptic and with suitable conditions on n(x,h), we establish a Harnack inequality for functions that are nonnegative in R(d) and harmonic in a domain. We also show that the Harnack inequality can fail without suitable conditions on n(x,h). A regularity theorem for those nonnegative harmonic functions is also proved.

引用

页码：21 / 44

页数：24

共 50 条

[1] Harmonic Functions for a Class of Integro-differential Operators
Mohammud Foondun
Potential Analysis, 2009, 31 : 21 - 44
[2] On some integro-differential operators in the class of harmonic functions and their applications
V. V. Karachik
B. Kh. Turmetov
B. T. Torebek
Siberian Advances in Mathematics, 2012, 22 (2) : 115 - 134
[3] MODIFIED RIEMANN-LIOUVILLE INTEGRO-DIFFERENTIAL OPERATORS IN THE CLASS OF HARMONIC FUNCTIONS AND THEIR APPLICATIONS
Torebek, Berikbol Tillabaiuly
UFA MATHEMATICAL JOURNAL, 2015, 7 (03): : 73 - 83
[4] Homogenization of a Class of Integro-Differential Equations with Levy Operators
Arisawa, Mariko
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (07) : 617 - 624
[5] NAKHUSHEV EXTREMUM PRINCIPLE FOR A CLASS OF INTEGRO-DIFFERENTIAL OPERATORS
Pskhu, Arsen
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2020, 23 (06) : 1712 - 1722
[6] Principal eigenvalues of a class of nonlinear integro-differential operators
Biswas, Anup
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (09) : 5257 - 5282
[7] Nakhushev Extremum Principle for a Class of Integro-Differential Operators
Arsen Pskhu
Fractional Calculus and Applied Analysis, 2020, 23 : 1712 - 1722
[8] On the Representation of Bicomplex Pseudoanalytic Functions by Integro-differential Operators
Berglez, Peter
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM-2015), 2016, 1738
[9] On the Spectrum of a Class of Integro-Differential Operators in L~p Space
宋德功
Chinese Science Bulletin, 1993, (18) : 1514 - 1517
[10] Subelliptic estimates for a class of degenerate elliptic integro-differential operators
Cancelier, C
Franchi, B
MATHEMATISCHE NACHRICHTEN, 1997, 183 : 19 - 41

← 1 2 3 4 5 →