Wirtinger Inequalities

Ravi Agarwal, Donal O’Regan and Samir Saker
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Ravi Agarwal: Texas A&M University–Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, School of Mathematics, Statistics, and Applied Mathematics
Samir Saker: Mansoura University, Department of Mathematics

Chapter Chapter 6 in Dynamic Inequalities On Time Scales, 2014, pp 229-241 from Springer

Abstract: Abstract The inequality of W. Wirtinger is given by 6.0.1 ∫ 0 1 y ′ ( t ) 2 d t ≥ π 2 ∫ 0 1 y 2 ( t ) d t $$\displaystyle{ \int _{0}^{1}\left (y^{{\prime}}(t)\right )^{2}dt \geq \pi ^{2}\,\int _{ 0}^{1}y^{2}(t)\mathrm{d}t }$$ for any y ∈ C 1[0, 1] such that y(0) = y(1) = 0.

Keywords: Wirtinger Type Inequality; Sturm-Liouville Eigenvalue Problem; Quadratic Inequality; Parts Formula; Lower Bound (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-11002-8_6

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