Quasi-convex Hamilton--Jacobi equations via limits of Finsler p-Laplace problems as p→ ∞

2021/07/06 by Hamza Ennaji, Ennaji, Hamza, Noureddine Igbida +3
Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2107.02606

openalex publication_date 2021/07/06 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the maximal viscosity solution of a class of quasi-convex Hamilton--Jacobi equations, coupled with inequality constraints on the boundary, can be recovered by taking the limit as p→∞ in a family of Finsler p-Laplace problems. The approach also enables us to provide an optimal solution to a Beckmann-type problem in general Finslerian setting and allows recovering a bench of known results based on the Evans--Gangbo technique.

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