- Research Article
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Applications of a Weighted Symmetrization Inequality to Elastic Membranes and Plates
Journal of Inequalities and Applications volume 2010, Article number: 808693 (2010)
This paper is devoted to some applications of a weighted symmetrization inequality related to a second order boundary value problem. We first interpret the inequality in the context of elastic membranes, and observe that it lends itself to make a comparison between the deflection of a membrane with a varying density with that of a membrane with a uniform density. Some mathematical consequences of the inequality including a stability result are presented. Moreover, a similar inequality where the underlying differential equation is of fourth order is also discussed.
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Emamizadeh, B. Applications of a Weighted Symmetrization Inequality to Elastic Membranes and Plates. J Inequal Appl 2010, 808693 (2010). https://doi.org/10.1155/2010/808693
- Differential Equation
- Fourth Order
- Stability Result
- Full Article
- Uniform Density