Electron. J. Diff. Equ., Vol. 2011 (2011), No. 165, pp. 1-8.

Consequences of Talenti's inequality becoming equality

Behrouz Emamizadeh, Mohsen Zivari-Rezapour

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.

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Behrouz Emamizadeh
Department of Mathematical Sciences
Xi'an Jiaotong-Liverpool University
Suzhou, Jiangsu 215123 China
email: Behrouz.Emamizadeh@xjtlu.edu.cn
Mohsen Zivari-Rezapour
Faculty of Mathematical and Computer Sciences
Shahid Chamran University, Ahvaz, Iran
email: mzivari@scu.ac.ir

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