A short proof of the \mathcal C^1,1 regularity for the eikonal equation

2024/09/08 by Radu Ignat, Ignat, Radu
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.05204

openalex publication_date 2024/09/08 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We give a short and self-contained proof of the interior \mathcal C^1,1 regularity of solutions φ:Ω→ ℝ to the eikonal equation |∇ φ|=1 in an open set Ω⊂ ℝ^N in dimension N≥ 1 under the assumption that φ is pointwise differentiable in Ω.

Related

• Global structure and regularity of solutions to the Eikonal equation
• Boundary regularity for the distance functions, and the eikonal equation
• Another regularizing property of the 2D eikonal equation
• Partial regularity for solutions to subelliptic eikonal equations
• Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets