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math.AP2023
A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications
Takashi Kagaya, Qing Liu, Hiroyoshi Mitake
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a…
math.AP2023
Discontinuous eikonal equations in metric measure spaces
Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely -integrable in the domai…