Existence and non-existence of maximizers for a class of weighted variational problems under equivalent constraints. Issue 5 (4th May 2023)

• Record Type: Journal Article
• Authors: Zhu, Maochun; Chen, Wenhuan
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 5(2023)
• Page Start: 793
• Page End: 820
• Publication Date: 2023-05-04
• Subjects: Weighted variational problems -- existence and non-existence -- Caffarelli–Kohn–Nirenberg inequalities; 46E35 -- 26D10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.2021195
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: In this paper, we study the existence and non-existence of maximizers for variational problems associated with Caffarelli–Kohn–Nirenberg-type inequalities under the equivalent constraints both in the subcritical case and critical case. Furthermore, if the maximizer exists, we can derive the concrete form of the maximizers. Our method is based on establishing a useful link between the attainability of the supremum in our variational problems and the attainability of the supremum of some special functions defined on ( 0, ∞ ) .