Equivalence of solutions of eikonal equation in metric spaces
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Publication:2216066
DOI10.1016/J.JDE.2020.10.018zbMATH Open1454.35051arXiv2005.13405OpenAlexW3094350434WikidataQ109994274 ScholiaQ109994274MaRDI QIDQ2216066
Author name not available (Why is that?)
Publication date: 15 December 2020
Published in: (Search for Journal in Brave)
Abstract: In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rectifiably connected metric spaces. The notions considered are that of curve-based viscosity solutions, slope-based viscosity solutions, and Monge solutions. By using the induced intrinsic (path) metric, we reduce the metric space to a length space and show the equivalence of these solutions to the associated Dirichlet boundary problem. Without utilizing the boundary data, we also localize our argument and directly prove the equivalence for the definitions of solutions. Regularity of solutions related to the Euclidean semi-concavity is discussed as well.
Full work available at URL: https://arxiv.org/abs/2005.13405
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