Work

On the sharp second order Caffarelli–Kohn–Nirenberg inequality

Year: 2025

Type: article

Abstract: The purpose of this paper is twofold. By developing a new technique, we first prove some sharp Caffarelli–Kohn–Nirenberg inequalities of second order for non-radial functions. As a direct consequence, we recover the sharp second order uncertainty principle in Cazacu, Flynn and Lam (2022). For the class of radial functions, we next establish a sharp inequality which can be regarded as the second order version of Xia's inequality (2007).

Source: Annales Fennici Mathematici

DOI: 10.54330/afm.161506

Authors: Anh Tuan Duong, Van Hoang Nguyen

Institutions: Trường Đại học Khoa học và Công nghệ Hà Nội, Hanoi University of Science and Technology, FPT University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Foundation for Science and Technology Development, Vietnam Institute for Advanced Study in Mathematics

Award: Tính chất định tính của phương trình đạo hàm riêng và bất đẳng thức hàm