A HARNACK INEQUALITY FOR FRACTIONAL LAPLACE EQUATIONS WITH LOWER ORDER TERMS

被引：74

作者：

Tan, Jinggang ^{[1
]}

Xiong, Jingang ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 31卷 / 03期

关键词：

Fractional Laplace equations; Harnack inequality; Moser's iteration;

D O I：

10.3934/dcds.2011.31.975

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.

引用

页码：975 / 983

页数：9

共 11 条

[1]

[Anonymous], 1997, Courant Lecture Notes

[2] Harnack inequalities for jump processes [J].

Bass, RF ;

Levin, DA .

POTENTIAL ANALYSIS, 2002, 17 (04) :375-388

[3]

CABRE X, ARXIV10120867V1

[4] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[5] Estimates on Green functions and Poisson kernels for symmetric stable processes [J].

Chen, ZQ ;

Song, RM .

MATHEMATISCHE ANNALEN, 1998, 312 (03) :465-501

[6] THE LOCAL REGULARITY OF SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

FABES, EB ;

KENIG, CE ;

SERAPIONI, RP .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1982, 7 (01) :77-116

[7] The Yamabe problem on manifolds with boundary: Existence and compactness results [J].

Han, ZC ;

Li, YY .

DUKE MATHEMATICAL JOURNAL, 1999, 99 (03) :489-542

[8] ON FUNCTIONS OF BOUNDED MEAN OSCILLATION [J].

JOHN, F ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (03) :415-&

[9]

Kassmann M., CLASSICAL HARNACK IN

[10] WEIGHTED NORM INEQUALITIES FOR FRACTIONAL INTEGRALS [J].

MUCKENHOUPT, B ;

WHEEDEN, RL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 192 :261-274

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