Regularity and Uniqueness of p-harmonic Maps with Small Range

2012/03/09 by Ali Fardoun, Fardoun, Ali, Rachid Regbaoui +1 · 2 citations
Mathematics · #35J20 #35J62 #35J70 #35J92 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #msc:35J20 #msc:35J62 #msc:35J70 #msc:35J92

paper · pdf · doi:10.48550/arxiv.1203.2101

15 pages

arxiv created 2012/03/09 · openalex publication_date 2012/03/09 · arxiv updated 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hoelder continuous derivatives. This gives an extension of a result by S. Hildebrandt et al concerning harmonic maps.

Cited by

• Sacks-Uhlenbeck type regularity for subcritical generalized p-harmonic maps into Homogeneous targets
• Higher dimensional Sacks-Uhlenbeck-type functionals and applications

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