| 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 |
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| 引用本文： | 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(中文版),2004(2). |
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| 作者姓名： | 何跃 |
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| 作者单位： | 复旦大学数学研究所 上海 |
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| 摘 要： | 本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.
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| 关 键 词： | 退化半线性椭圆型方程 适定性 正则性 先验估计 |
WELL-POSEDNESS AND REGULARITY OF BOUNDARY VAULE PROBLEMS FOR A CLASS OF SECOND ORDER DEGENERATE SEMILINEAR ELLIPTIC EQUATIONS |
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| HE Yue
Institute of Mathematics,Fudan University,Shanghai ,China, School of Mathematics and Computer Science,Nanjing Normal University,Nanjing ,China..WELL-POSEDNESS AND REGULARITY OF BOUNDARY VAULE PROBLEMS FOR A CLASS OF SECOND ORDER DEGENERATE SEMILINEAR ELLIPTIC EQUATIONS[J].Chinese Annals of Mathematics,2004(2). |
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| Authors: | HE Yue
Institute of Mathematics Fudan University Shanghai China School of Mathematics and Computer Science Nanjing Normal University Nanjing China |
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| Institution: | HE Yue
Institute of Mathematics,Fudan University,Shanghai 200433,China, School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China. |
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| Abstract: | |
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| Keywords: | Degenerate semilinear elliptic equation Well-posedness Regularity Priori estimate |
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