Structure of minimizers of Cafarelli-Kohn-Nirenberg inequality

Abstract

In this article, we are concerned with radial solutions for the best constant of the Cafarelli-Kohn-Nirenberg inequality. Firstly, we classify the radial solutions according to its asymptotic behavior as $r \to 0$ and $r \to \infty$. Secondly, we investigate the structure of radial singular solutions. Lastly, we briefly discuss the Neumann problem related to the Cafarelli-Kohn-Nirenberg inequality.