A regularizing property of the 2D-eikonal equation

2014/09/07 by Camillo De Lellis, Radu Ignat, De Lellis, Camillo +1 · 1 citation
Mathematics · #35F21 #35L65 #46E35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems #math.AP #msc:35F21 #msc:35L65 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1409.2102

14 pages, 3 figures

arxiv created 2014/09/07 · openalex publication_date 2014/09/07 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any 2-dimensional solution ψ∈ W_loc^{1+\frac 1 3, 3} of the eikonal equation has locally Lipschitz gradient ∇ ψ except at a locally finite number of vortices.

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