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math.AP2025
On the Gromov--Hausdorff stability of metric viscosity solutions
Shimpei Makida
We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of met…
math.AP2023
Stability of metric viscosity solutions under Hausdorff convergence
Shimpei Makida, Atsushi Nakayasu
This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain pe…
math.AP2023
Stability of viscosity solutions on expanding networks
Shimpei Makida
In this paper, we prove the stability of viscosity solutions of the Hamilton--Jacobi equations for a sequence of networks embedded in Euclidean space. The network considered in thi…