椭圆方程的很弱解估计

journal6 ›› 2005, Vol. 26 ›› Issue (3): 13-19.

椭圆方程的很弱解估计

(湖南师范大学数学与计算机科学学院，湖南长沙 410081)

出版日期:2005-07-15 发布日期:2012-09-22

Estimates for Very Weak Solutions to Elliptic Equations

(Department of Mathematics,Hunan Normal University,Changsha 410081,China)

Online:2005-07-15 Published:2012-09-22
About author:ZHOU Shu-qing（1968-),male,was born in Shaoyang County,Hunan Province,Ph.D.,associate professor of Department of Mathematics,Hunan Normal University;research area is partial differential equations.
Supported by:
The National Natural Science Foundation of China(A0324632)

摘要/Abstract

摘要：利用以极大函数表示的关于Sobolev函数的一个逐点估计，来构造全局的Lipschitz连续的检验函数，并利用Hardy不等式，得到方程－div A（ｘ，Du）＋B（ｘ，u）＝div（｜F｜p-2F）在一定条件下的很弱解全局估计.作为推论，得出方程-div A（ｘ，Du）=0在零边值条件下只有零解.

关键词： Hardy不等式, 很弱解, Lipschitz, 连续, 全局估计

Abstract: Using a pointwise inequality for Sobolev functionsin terms of maximum function to construct a global Lipschitz continuous testing function and using Hardy’s inequality,the author obtains global estimates for very weak solutions to quasi-linear elliptic equation div A(x，Du)+B(x，u)=－div(｜F｜p－2F) satisfying certain conditions listing in the following.

Key words: Hardy&rsquo, s inequality, very weak solution, Lipschitz continuous, global estimate

周树清, 邹锐标, 向占宏, 陈大学. 椭圆方程的很弱解估计[J]. journal6, 2005, 26(3): 13-19.

ZHOU Shu-Qing, ZOU Rui-Biao, XIANG Zhan-Hong, CHEN Da-Xue. Estimates for Very Weak Solutions to Elliptic Equations[J]. journal6, 2005, 26(3): 13-19.

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