A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications
Takashi Kagaya, Qing Liu, Hiroyoshi Mitake · arXiv (Cornell University) · 2023
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 class of nonlocal Hamilton--Jacobi equations and establish a control-based representation formula for solutions. We also apply the formula to discuss the fattening phenomenon and large-time asymptotics of the solutions.