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

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].

Cited by in corpus (4)

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• Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces
• Equivalence of solutions of eikonal equation in metric spaces