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arXiv · 1407.7634

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

Atsushi Nakayasu
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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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Atsushi Nakayasu. 2014-07-29. On metric viscosity solutions for Hamilton-Jacobi equations of evolution type. https://arxiv.org/abs/1407.7634

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