一类非齐次障碍问题的很弱解的局部可积性

J4 ›› 2010, Vol. 45 ›› Issue (8): 66-70.

一类非齐次障碍问题的很弱解的局部可积性

李娟

宁波大学理学院, 浙江宁波 315211

收稿日期:2009-09-28 出版日期:2010-08-16 发布日期:2010-09-16
作者简介:李娟(1977-),女,博士,讲师,主要从事复分析和偏微分方程的研究. Email:juanjuan-li@163.com
基金资助:
国家自然科学基金资助项目(60872095); 宁波市自然科学基金资助项目(2008A610018)；宁波市科研基金资助项目（2009B21003）

Local integrability for very weak solutions of nonhomogeneous obstacle problems

LI Juan

Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang, China

Received:2009-09-28 Online:2010-08-16 Published:2010-09-16

摘要/Abstract

摘要：

给出了二阶非齐次椭圆方程
-divA(x,▽u)=f(x),u∈K^r_ψ,θ (Ω)
的障碍问题很弱解的定义, 并利用Hodge分解,证明了上面提到的障碍问题很弱解的高阶可积性结果。

关键词: 障碍问题;椭圆方程;Hodge分解

Abstract:

A definition of very weak solutions to obstacle problem of a second-order nonhomogeneous elliptic equation
-divA(x,▽u)=f(x),u∈K^r_ψ,θ (Ω)
is given, and a higher integrability result about very weak solution to the above mentioned obstacle problem via Hodge decomposition is proved.

Key words: obstacle problem; elliptic equation; Hodge decomposition

李娟. 一类非齐次障碍问题的很弱解的局部可积性[J]. J4, 2010, 45(8): 66-70.

LI Juan. Local integrability for very weak solutions of nonhomogeneous obstacle problems[J]. J4, 2010, 45(8): 66-70.

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