Applications of a Weighted Symmetrization Inequality to Elastic Membranes and Plates
© Behrouz Emamizadeh. 2010
Received: 28 January 2010
Accepted: 10 June 2010
Published: 28 June 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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