Vectorial Kato inequality for p-harmonic maps with optimal constant

2025/03/06 by Gastel, Andreas, Mazowiecka, Katarzyna, Miśkiewicz, Michał
#35B65 #35J60 #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.05038

Abstract

We derive the sharp vectorial Kato inequality for p-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued p-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how this inequality can be used in the study of regularity of p-harmonic maps. Furthermore, in the case of p-harmonic maps from B³ to \mathbbS³, we enhance the known range of p values for which regularity is achieved. Specifically, we establish that for p ∈ [2, 2.642], minimizing p-harmonic maps must be regular.

Related

• Regularity of minimizing p-harmonic maps into spheres and sharp Kato inequality
• Examples of p-harmonic maps
• Refined Kato inequalities and conformal weights in Riemannian geometry
• Quantitative regularity for p-harmonic maps
• Gradient estimate and Liouville theorems for p-harmonic maps