Radial Limits of Nonparametric PMC Surfaces with Intermediate Boundary\n Curvature

2019/09/10 by Kirk E. Lancaster, Lancaster, Kirk, Mozhgan Nora Entekhabi +1
Computer Science · Mathematics · #53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary: 35J67 #Secondary: 35J93

paper · pdf · doi:10.48550/arxiv.1909.04741

openalex publication_date 2019/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the boundary behavior of the variational solution f of a\nDirichlet problem for a prescribed mean curvature equation in a domain\n\Ω\⊂ bf R² near a point \O\∈\∂\Ω under\ndifferent assumptions about the curvature of \∂\Ω on each side of\n\O. We prove that the radial limits at \O of f exist\nunder different assumptions about the Dirichlet boundary data \φ, depending\non the curvature properties of \∂\Ω near \O.\n

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