Optimal regularity results for the one-dimensional prescribed curvature equation via the strong maximum principle

2022/05/24 by Julián López-Gómez, Lopez-Gomez, Julian, Pierpaolo Omari +1
Computer Science · Mathematics · #34B15 #35B50 #35B65 #35J93 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2205.11936

openalex publication_date 2022/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A refined version of the strong maximum principle is proven for a class of second order ordinary differential equations with possibly discontinuous non-monotone nonlinearities. Then, exploiting this tool, some optimal regularity results recently established by Lopez-Gomez and Omari, for the bounded variation solutions of non-autonomous quasilinear equations driven by the one-dimensional curvature operator, are substantially improved by admitting general prescribed curvatures and by incorporating general boundary conditions. The new approach developed here yields a new, deeper, interpretation of the assumptions introduced in our previous papers, simultaneously clarifying their meaning and making fully transparent their connection with the strong maximum principle.

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