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一类退化椭圆算子的Harnack不等式
  • ISSN号：1671-6841
  • 期刊名称：《郑州大学学报：理学版》
  • 时间：0
  • 分类：O175.25[理学—数学;理学—基础数学]
  • 作者机构：[1]西北工业大学应用数学系
  • 相关基金：国家自然科学基金资助项目,编号10871157
作者： 崔学伟[1]
关键词： Hrmander向量场, HARNACK不等式, Hlder连续性, 退化Morrey空间, Hrmander vector field, Harnack s inequality, Hlder continuity, degenerate Morrey space
中文摘要：

研究了形式如下的一类由H rmander向量场构成的退化椭圆方程∑mi,j=1Xi*(aij(x)Xju+diu)+∑mi=1biXiu+eu=f-∑mi=1Xifi,在方程的低阶项的系数属于退化Morrey空间的假定下,利用加权的Sobolev不等式、退化Morrey空间的加权的嵌入引理和经典的Moser迭代方法,证明了方程的弱解是局部有界的,得到了方程的非负弱解的Harnack不等式,从而得到了方程弱解的H lder连续性.欧氏空间退化椭圆方程的一些结果被推广到H rmander向量场的情形.

英文摘要：

A class of degenerate elliptic equations formed by Hrmander vector fields of the form ∑mi,j=1X*i(aij(x)Xju+diu)+∑mi=1biXiu+eu=f∑mi=1Xifi,are studied.By weighted Sobolev inequality,weighted embedding lemma related to degenerate Morrey space and classic Moser s iteration method,local boundedness of weak solution and Harnack s inequality for nonnegative weak solution are proved under the assumption that the coefficients of the lower order terms are in degenerate Morrey space.As a consequence,local Hlder cont...

同期刊论文项目
退化椭圆偏微分方程的Morrey正则性与齐次群上的奇异积分方法
期刊论文 34
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期刊信息
  • 《郑州大学学报：理学版》
  • 中国科技核心期刊
  • 主管单位:河南省教育厅
  • 主办单位:郑州大学
  • 主编：李燕燕
  • 地址：郑州市高新区科学大道100号
  • 邮编：450001
  • 邮箱：lixueban@zzu.edu.cn
  • 电话：0371-67781272
  • 国际标准刊号：ISSN：1671-6841
  • 国内统一刊号：ISSN：41-1338/N
  • 邮发代号:36-191
  • 获奖情况:
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,美国数学评论（网络版）,波兰哥白尼索引,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,英国英国皇家化学学会文摘
  • 被引量:2791