Analytical properties for degenerate equations
Analytical properties for degenerate equations
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简并方程的解析性质
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
W. Minicozzi
中科院分区：
文献类型：
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作者：
T. Colding;W. Minicozzi
根据经典的结果，解析椭圆型偏微分方程的解，如拉普拉斯方程，是解析的.在许多情况下，来自分析的性质比分析性本身更重要。许多重要的方程都是退化椭圆型方程，其解的正则性要低得多。尽管如此，人们还是希望解具有解析函数的性质。这些属性与重要的开放问题密切相关。在本综述中，我们将解释为什么一个重要的退化椭圆方程的解具有解析性质，即使其解甚至不是C^3 $。
By a classical result, solutions of analytic elliptic PDEs, like the Laplace equation, are analytic. In many instances, the properties that come from being analytic are more important than analyticity itself. Many important equations are degenerate elliptic and solutions have much lower regularity. Still, one may hope that solutions share properties of analytic functions. These properties are closely connected to important open problems. In this survey, we will explain why solutions of an important degenerate elliptic equation have analytic properties even though the solutions are not even $C^3$.
Ornstein-Uhlenbeck 算子特征函数的尖锐频率界限
DOI：
10.1007/s00526-018-1405-z
发表时间：
2018
影响因子：
2.1
作者：
Colding, Tobias Holck;Minicozzi, William P.
通讯作者：
Minicozzi, William P.