On metric viscosity solutions for Hamilton-Jacobi equations of evolution type

2014/07/29 by Atsushi Nakayasu, Nakayasu, Atsushi · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35D40 #35F21 #35F25 #49L20 #49L25 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Variational Analysis #math.AP #msc:35D40 #msc:35F21 #msc:35F25 #msc:49L20 #msc:49L25

paper · pdf · doi:10.48550/arxiv.1407.7634

arxiv created 2014/07/29 · openalex publication_date 2014/07/29 · arxiv updated 2014/07/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems. We also note a relationship between the notion of a solution and another notion based on characterization of the modulus of the gradient in the sense of [13].

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• Stability properties and large time behavior of viscosity solutions of Hamilton-Jacobi equations on metric spaces

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