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Applications of a Weighted Symmetrization Inequality to Elastic Membranes and Plates

Abstract

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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Correspondence to Behrouz Emamizadeh.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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

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  • DOI: https://doi.org/10.1155/2010/808693

Keywords

  • Differential Equation
  • Fourth Order
  • Stability Result
  • Full Article
  • Uniform Density