Wirtinger Inequalities

Abstract

The inequality of W. Wirtinger is given by

$$\displaystyle{ \int _{0}^{1}\left (y^{{\prime}}(t)\right )^{2}dt \geq \pi ^{2}\,\int _{ 0}^{1}y^{2}(t)\mathrm{d}t }$$

(6.0.1)

for any y ∈ C ¹[0, 1] such that y(0) = y(1) = 0.