Hamilton-Jacobi equations in metric spaces

Qing Liu; Xiaodan Zhou

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arXiv · 2308.08073

Hamilton-Jacobi equations in metric spaces

Qing Liu·Xiaodan Zhou

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Abstract

These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few important results concerning the well-posedness of Hamilton-Jacobi equations in metric spaces, especially several recently proposed notions of metric viscosity solutions to the eikonal equation. Basic knowledge about metric spaces and a review of viscosity solution theory in the Euclidean spaces are also presented.

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Qing Liu, Xiaodan Zhou. 2023-08-15. Hamilton-Jacobi equations in metric spaces. https://arxiv.org/abs/2308.08073

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