Consequences of Talenti's inequality becoming equality

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.

Keywords

• Talenti's inequality
• p-Laplacian operator
• elastic membrane
• rearrangement maximization
• unique optimal solution