Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

被引：1

作者：

Polidoro, Sergio ^{[1
]}

Ragusa, Maria Alessandra ^{[2
]}

机构：

[1] Univ Modena & Reggio Emilia, Dipartimento Matemat Pura & Applicata, I-41100 Modena, Italy

[2] Univ Catania, Dipartmento Matemat, I-95125 Catania, Italy

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2008年 / 24卷 / 03期

关键词：

Hypoelliptic operator; Schrodinger equation; Harnack inequality; Green function;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L(0)u + Vu = 0, where L-0 is a linear second order hypoelliptic operator and V belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem.

引用

页码：1011 / 1046

页数：36

共 50 条

[41] THE HARNACK INEQUALITY AND RELATED PROPERTIES FOR SOLUTIONS OF ELLIPTIC AND PARABOLIC EQUATIONS WITH DIVERGENCE-FREE LOWER-ORDER COEFFICIENTS
Nazarov, A. I.
Ural'tseva, N. N.
ST PETERSBURG MATHEMATICAL JOURNAL, 2012, 23 (01) : 93 - 115
[42] HARNACK INEQUALITY FOR DEGENERATE PARABOLIC EQUATIONS
GUTIERREZ, CE
WHEEDEN, RL
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (4-5) : 745 - 770
[43] A HARNACK INEQUALITY FOR DEGENERATE PARABOLIC EQUATIONS
CHIARENZA, FM
SERAPIONI, RP
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1984, 9 (08) : 719 - 749
[44] A Harnack inequality for ordinary differential equations
Berhanu, S
Mohammed, A
AMERICAN MATHEMATICAL MONTHLY, 2005, 112 (01): : 32 - 41
[45] DEGENERATE PARABOLIC EQUATIONS AND HARNACK INEQUALITY
CHIARENZA, F
SERAPIONI, R
ANNALI DI MATEMATICA PURA ED APPLICATA, 1984, 137 : 139 - 162
[46] HARNACK INEQUALITY FOR PARABOLIC DIFFERENTIAL EQUATIONS
MOSER, J
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1964, 17 (01) : 101 - &
[47] THE PARABOLIC HARNACK INEQUALITY FOR NONLOCAL EQUATIONS
Kassmann, Moritz
Weidner, Marvin
DUKE MATHEMATICAL JOURNAL, 2024, 173 (17) : 3413 - 3451
[48] HARNACK TYPE INEQUALITY FOR SOLUTIONS TO NON LINEAR ELLIPTICAL EQUATIONS OF HIGHER ORDER
D'Asero, Salvatore
MATEMATICHE, 2005, 60 (02): : 451 - 454
[49] HARNACK INEQUALITY FOR WEAK SOLUTIONS OF QUASILINEAR PAROBOLIC SECOND-ORDER EQUATIONS
IVANOV, AV
DOKLADY AKADEMII NAUK SSSR, 1967, 173 (04): : 752 - &
[50] Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations
Huang, Xing
Ma, Xiaochen
JOURNAL OF THEORETICAL PROBABILITY, 2024, 37 (04) : 3152 - 3176

← 1 2 3 4 5 →