关于变步长情形下离散函数的一些内插不等式

Some interpolation inequalities with the variable step of discrete functions

在研究偏微分方程解的适定性方面,Sobolev空间中的嵌入定理和内插不等式起着非常重要的作用。许多著名学者通过等距分割已经得到了比较好的嵌入定理和内插不等式并进行了证明,文[1]研究了一元离散函数中间差商的若干内插不等式,文[2]研究了三元离散函数中间差商的若干内插不等式。证明了一元离散函数和三元离散函数在不等距分割下也相应满足这些嵌入定理和内插不等式。

The imbedding theorems and the interpolation inequalities for the functions in Soblev spaces play a very important role in the study of the well posedness of partial differential equations and systems. Some famous experts investigated and established the better imbedding theorems and interpolation inequalities for when the finite interval is divided into the same small segment grids. For example, the interpolation inequalities for discrete functions with only one index and three indexes are derived in [ 1 ] and [ 2 ], respectively. The authors establish the interpolation formulas for the functions with one index （respectively, three indexes） of Soblev spaces on the variable step.