Theorems in analysis | Inequalities

Agmon's inequality

In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon, consist of two closely related interpolation inequalities between the Lebesgue space and the Sobolev spaces . It is useful in the study of partial differential equations. Let where . 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 where . Then Agmon's inequality in 2D states that there exists a constant such that For the -dimensional case, choose and such that . Then, if and , the following inequality holds for any (Wikipedia).

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From playlist Solve Absolute Value Inequalities

Related pages

Interpolation inequality | Brezisโ€“Gallouet inequality | Lp space | Sobolev space | Partial differential equation | Mathematical analysis