On the boundary Hölder regularity for the infinity Laplace equation

2019/01/18 by Leyun Wu, Wu, Leyun, Yuanyuan Lian +3
Computer Science · Mathematics · #35B50 #35B65 #35J25 #35J67 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35B50 #msc:35B65 #msc:35J25 #msc:35J67

paper · pdf · doi:10.48550/arxiv.1901.06131

arxiv created 2019/01/18 · openalex publication_date 2019/01/18 · arxiv updated 2019/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove the boundary Hölder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exterior cone condition, the Reifenberg flat domains, and the corkscrew domains (including the non-tangentially accessible domains) are special cases. The key idea, following [3], is that the strong maximum principle and the scaling invariance imply the boundary Hölder regularity.

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