In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon,[1] consist of two closely related interpolation inequalities between the Lebesgue space
{\displaystyle L^{\infty }}
and the Sobolev spaces
.
It is useful in the study of partial differential equations.
[vague].
Then Agmon's inequalities in 3D state that there exists a constant
such that and In 2D, the first inequality still holds, but not the second: let
Then Agmon's inequality in 2D states that there exists a constant
-dimensional case, choose
0 < θ < 1
= θ
+ ( 1 − θ )
, the following inequality holds for any
This mathematical analysis–related article is a stub.
You can help Wikipedia by expanding it.