Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 165, pp. 1-8.

Title: Consequences of Talenti's inequality becoming equality

Authors: Behrouz Emamizadeh (Xian Jiaotong-Liverpool Univ., China)
         Mohsen Zivari-Rezapour (Shahid Chamran Univ., Ahvaz, Iran)

Abstract:
 In this article, we consider the case of equality in a well known
 inequality for the  p-Laplacian due to Giorgio Talenti.
 Our approach seems to be simpler than the one by Kesavan [6].
 We use a result from rearrangement optimization to prove
 the main result in this article. Some physical interpretations
 are also presented.
	 
Submitted June 14, 2011. Published December 13, 2011.
Math Subject Classifications: 35J62, 35P30, 35Q74, 35A99, 49J20.
Key Words: Talenti's inequality; p-Laplacian operator;
           elastic membrane; rearrangement maximization; 
	   unique optimal solution.