The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle

2021/02/02 by Anh Tuan Duong, Duong, Anh Tuan, Van Hoang Nguyen +1 · 1 citation
Mathematics · Engineering · Computer Science · #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2102.01425

Abstract

In this paper we prove a class of second order Caffarelli-Kohn-Nirenberg inequalities which contains the sharp second order uncertainty principle recently established by Cazacu, Flynn and Lam \citeCFL2020 as a special case. We also show the sharpness of our inequalities for several classes of parameters. Finally, we prove two stability versions of the sharp second order uncertainty principle of Cazacu, Flynn and Lam by showing that the difference of both sides of the inequality controls the distance to the set of extremal functions in L² norm of gradient of functions.

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• On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking

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