2024/10/01 by Yingfang Zhang, Wenming Zou, Zhang, Yingfang +1 · 1 citation
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Contact Mechanics and Variational Inequalities #Nonlinear Partial Differential Equations
paper · pdf · doi:10.1016/j.na.2026.114074
We study the stability of a class of Caffarelli-Kohn-Nirenberg (CKN) interpolation inequality and establish a strong-form stability as following: inf_v\inMp,a,b\frac ‖u-v‖Hbp ‖u-v‖Lpap-1 ‖u‖Hpb‖u‖Lpap-1 ≤ Cδp,a,b(u)t, where t=1 for p=2 and t=(1)/(p) for p > 2, and δp,a,b(u) is deficit of the CKN. We also note that it is impossible to establish stability results for ‖⋅‖Hbp or ‖⋅‖Lap separately. Moreover, we consider the second-order CKN inequalities and establish similar results for radial functions.