Open Access

Applications of a Weighted Symmetrization Inequality to Elastic Membranes and Plates

Journal of Inequalities and Applications20102010:808693

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

Received: 28 January 2010

Accepted: 10 June 2010

Published: 28 June 2010

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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Authors’ Affiliations

(1)
Department of Mathematics, The Petroleum Institute

Copyright

© Behrouz Emamizadeh. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.