WEIGHTED POINCARE INEQUALITIES FOR HORMANDER VECTOR-FIELDS AND LOCAL REGULARITY FOR A CLASS OF DEGENERATE ELLIPTIC-EQUATIONS

被引：30
作者：
FRANCHI, B
LU, G
WHEEDEN, RL
机构：
[1] WRIGHT STATE UNIV,DEPT MATH,DAYTON,OH 45435
[2] RUTGERS STATE UNIV,DEPT MATH,NEW BRUNSWICK,NJ 08903
[3] INST ADV STUDY,PRINCETON,NJ 08540
来源：
POTENTIAL ANALYSIS | 1995年 / 4卷 / 04期
关键词：
HORMANDER VECTOR FIELDS; POINCARE INEQUALITY; RELATIVE ISOPERIMETRIC INEQUALITY; HARNACKS INEQUALITY;
D O I：
10.1007/BF01053453
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we state weighted Poincare inequalities associated with a family of vector fields satisfying Hormander rank condition. Then, applications are given to relative isoperimetric inequalities and to local regularity (Harnack's inequality) for a class of degenerate elliptic equations with measurable coefficients.
引用
收藏
页码：361 / 375
页数：15
相关论文
共 36 条
[31]   BALLS AND METRICS DEFINED BY VECTOR-FIELDS .1. BASIC PROPERTIES [J].
NAGEL, A ;
STEIN, EM ;
WAINGER, S .
ACTA MATHEMATICA, 1985, 155 (1-2) :103-147
[32]   HYPOELLIPTIC DIFFERENTIAL OPERATORS AND NILPOTENT GROUPS [J].
ROTHSCHILD, LP ;
STEIN, EM .
ACTA MATHEMATICA, 1976, 137 (3-4) :247-320
[33]  
SALOFFCOSTE L, 1992, DUKE MATH J, V65, P27
[34]   FUNDAMENTAL-SOLUTIONS AND GEOMETRY OF THE SUM OF SQUARES OF VECTOR-FIELDS [J].
SANCHEZCALLE, A .
INVENTIONES MATHEMATICAE, 1984, 78 (01) :143-160
[35]   WEIGHTED INEQUALITIES FOR FRACTIONAL INTEGRALS ON EUCLIDEAN AND HOMOGENEOUS SPACES [J].
SAWYER, E ;
WHEEDEN, RL .
AMERICAN JOURNAL OF MATHEMATICS, 1992, 114 (04) :813-874
[36]   REGULARITY FOR QUASI-LINEAR 2ND-ORDER SUBELLIPTIC EQUATIONS [J].
XU, CJ .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (01) :77-96
1234