Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 551-567

Title STRUCTURE OF MINIMIZERS OF CAFARELLI-KOHN-NIRENBERG INEQUALITY

Author Jann-Long Chern, Chih-Her Chen and Gyeongha Hwang

(Received March 1, 2019, revised August 27, 2019)
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.

Mathematics Subject Classification. Primary 35J91; Secondary 35A20.
Key words and phrases. The best constant, Cafarelli-Kohn-Nirenberg inequality, radial solution, singular solution, Pohozaev identity.

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