A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS
A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS
复制标题
关于弱和强退化微分算子的加权 Sobolev 空间的注记
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Yue Wang
中科院分区：
文献类型：
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作者：
P. Kogut;O. Kupenko;G. Leugering;Yue Wang
本文讨论了一类特殊的加权Sobolev空间的Poincaré不等式的有关问题。这些空间的一个共同特征是，它们可以自然地与具有可变扩散系数的非一致椭圆微分算子相关联。我们给出了这些空间的分类在1-D的情况下，相应的权重系数退化的措施的基础上，并研究其关键性质。
In this paper we discuss some issues related to Poincaré’s inequality for a special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties.