QUALITATIVE PROPERTIES FOR ELLIPTIC PROBLEMS WITH CKN OPERATORS
2023 年 77 巻 2 号 p. 385-400
詳細
2023 年 77 巻 2 号 p. 385-400
The purpose of this paper is to study the basic properties of a degenerate operator with critical gradient and critical Hardy term, controlled by two free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of singular solutions with isolated singularities of the related Poisson problem in a bounded domain containing the origin.
