Liouville theorem for X-elliptic operators

被引：31

作者：

Kogoj, Alessia Elisabetta ^{[1
]}

Lanconelli, Ermanno ^{[1
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, IT-40126 Bologna, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 08期

关键词：

Liouville theorems; Subelliptic equations; Degenerate elliptic equations; LIE-GROUPS; SPACES; INEQUALITIES;

D O I：

10.1016/j.na.2008.12.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Liouville-type theorem for a class of degenerate elliptic operators of the form Lu := Sigma(N)(ij=1) partial derivative(xi) (a(ij)partial derivative(xj)u) + Sigma(N)(i=1)bi partial derivative(xi)u. L is supposed to be X-elliptic, with respect to a family X = (X(1) , ... , X(m)) of locally Lipschitz continuous vector fields, in the sense introduced in [E. Lanconelli, A.E. Kogoj, X-elliptic operators and X-control distances, Contributions in Honor of the Memory of Ennio De Giorgi, Ricerche di Matematica 49 (Suppl.) (2000) 223-243]. (c) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2974 / 2985

页数：12

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