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Sobolev不等式关于梯度的最优稳定性（张翼）
Sobolev不等式 梯度 最优稳定性
2023/2/22
We prove a sharp quantitative version of the p-Sobolev inequality for any 1ol on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent... 
Let M be a cg-connected manifold. Let L be a second-order
differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L
has no zero-order term). Assume that there exists a posi...
在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.
Generalized Dunkl-Sobolev Spaces of Exponential Type and Applications
Dunkl operators Dunkl-Bessel-Laplace operator Generalized Dunkl-Sobolev spaces of exponential type Pseudo differential-difference operators Reproducing kernels
2010/1/22
We study the Sobolev spaces of exponential type associated with the Dunkl-Bessel Laplace operator. Some properties including completeness and the imbedding theorem are proved. We next introduce a clas...