Heisenberg群上次椭圆p-Laplace方程的边界估计  

Boundary Estimates of Subelliptic p-Laplace Equations on the Heisenberg Group

作　　者：刘海峰[1] 钮鹏程[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《数学年刊（A辑）》2008年第1期135-142,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10371099)资助的项目

摘　　要：研究次椭圆p-Laplace方程(p>1)解的边界性质,通过建立Heisenberg群上带有区域内点到边界Carnot-Carathéodory距离函数的Hardy型不等式,给出了有界域上次椭圆p-Laplace方程以及带非平凡位势的次椭圆p-Laplace方程的解在边界附近的若干估计.This paper studies the boundary properties of solutions to subelliptic p-Laplace equations. By constructing Hardy type inequalities involving the Carnot-Carathéodory distance from interior point to the boundary of a domain on the Heisenberg group, the authors prove some LP-estimates near the boundary of subelliptic p-Laplace equations and subelliptic p-Laplace equations with nontrivial potentials.

关 键 词：次椭圆p-Laplace方程 HEISENBERG群 HARDY不等式 

分 类 号：O175.25[理学—数学]