2023/02/13 by Katarzyna Mazowiecka, Mazowiecka, Katarzyna, Michał Miśkiewicz +1
Computer Science · Mathematics · #35J92 #53C43 #58E20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2302.06738
openalex publication_date 2023/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study regularity of minimizing p-harmonic maps u \colon B3 → \mathbbS3 for p in the interval [2,3]. For a long time, regularity was known only for p = 3 (essentially due to Morrey) and p = 2 (Schoen-Uhlenbeck), but recently Gastel extended the latter result to p ∈ [2,2+(2)/(15)] using a version of Kato inequality. Here, we establish regularity for a small interval p∈ [2.961,3] by combining Morrey's methods with Hardt and Lin's Extension Theorem. We also improve on the other result by obtaining regularity for p ∈ [2,p0] with p0 = (3+√(3))/(2) ≈ 2.366. In relation to this, we address a question posed by Gastel and prove a sharp Kato inequality for p-harmonic maps in two-dimensional domains, which is of independent interest.