[1]何 跃.一类退化椭圆型方程Dirichlet问题的解的高阶正则性[J].南京师大学报(自然科学版),2007,30(01):28-32.
　He Yue.High Order Regularity of Solutions to the Dirichlet Problem for a Class of Degenerate Elliptic Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2007,30(01):28-32.
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一类退化椭圆型方程Dirichlet问题的解的高阶正则性()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第30卷
期数:
2007年01期
页码:
28-32
栏目:
数学
出版日期:
2007-03-30

文章信息/Info

Title:
High Order Regularity of Solutions to the Dirichlet Problem for a Class of Degenerate Elliptic Equations
作者:
何 跃1;  2
1.中山大学数学与计算科学学院 广东广州510275
2. 南京师范大学数学与计算机科学学院数学研究所, 江苏南京210097
Author(s):
He Yue1; 2
1.School of Mathematics and Computing Science,Zhongshan University,Guangzhou 510275,China
2. In stitu te ofM ath em at ics, School ofM athem atics and Com pu ter Science, Nanj ing Norm alUn iversity, Nan jing 210097, Ch ina
关键词:
退化椭圆型方程;  退化抛物型方程;  有界周期区域;  Dirichlet问题;  极小图;  刚性问题;  解的高阶正则性
Keywords:
degene rate e lliptic equa tions;  degenerate parabo lic equations;  bounded periodic dom ain;  Dir ichlet prob lem;  m inim a l g raphs;  r ig id ity problem;  h igh order regularity o f so lutions
分类号:
O175.25
摘要:
由于退化椭圆型方程的研究与双曲空间中极小图的Dirichlet问题,以及曲面的无穷小等距形变刚性问题的密切联系,在有界周期域上讨论了一类退化椭圆型方程Dirichlet问题的解的高阶正则性,利用泛函分析方法得到一个涉及解的高阶正则性的充分必要条件.
Abstract:
Since the study of degenerate e lliptic equation is very c losely re lated to theD irich let prob lem for m in im al graphs in hyperbolic space and the r ig id ity problem arising from in finitesim a l isom etr ic de fo rm ation of sur faces, w e discuss the high order regular ity o f so lu tions to the Dir ichlet problem fo r a class o f degenerate e lliptic equations in a bounded per iod ic dom a in. By them ethods o f functiona l ana lysis, w e ge t a suffic ient and necessary cond ition, wh ich concerns the h igh order regular ity of so lutions for such problem s.

参考文献/References:

[ 1] Lin F H. On the Dir ichlet prob lem for m inim a l g raphs in hyperbo lic space[ J]. InventM a th, 1989, 96: 592-612.
[ 2] Daska lopou los P, H am ilton R. Regu la rity of the free bounda ry for the n-d im ensiona l po rous m ed ium equa tion[ J]. J Am er M a th Soc, 1998, 11: 899-965.
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[ 7] 雷雨田. 具变系数的G inzbu rg- landau泛函径向极小元[ J]. 南京师大学报: 自然科学版, 2004, 27( 1) : 1-6.
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[ 9] 何跃. 一类二阶退化半线性椭圆型方程边值问题的适定性及解的正则性[ J]. 数学年刊A 辑, 2004, 25( 2): 225-242.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金面上基金( 10571087)、江苏省教育厅自然科学基金( 04K JB110062)资助项目.
作者简介: 何 跃( 1970) ) , 博士后, 主要从事非线性偏微分方程和微分几何的教学与研究. E-mail:heyue@ n jnu. edu. cn
更新日期/Last Update: 2013-05-05