Hamilton-Jacobi equations with monotone nonlinearities on convex cones

2022/06/25 by Hongbin Chen, Jiaming Xia, Chen, Hong-Bin +1 · 1 citation
Computer Science · Mathematics · #35A01 #35A02 #35D40 #35F21 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2206.12537

openalex publication_date 2022/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas.

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