Gradient stability for the Sobolev inequality: the case p≥ 2

2015/10/07 by Figalli, Alessio, Neumayer, Robin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.02119

Abstract

We prove a strong form of the quantitative Sobolev inequality in ℝⁿ for p≥ 2, where the deficit of a function u∈ W^1,p controls ‖ ∇ u -∇ v‖_L^p for an extremal function v in the Sobolev inequality.

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