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arXiv · 2310.00925

A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications

Takashi Kagaya·Qing Liu·Hiroyoshi Mitake
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Abstract

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.

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Takashi Kagaya, Qing Liu, Hiroyoshi Mitake. 2023-10-02. A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications. https://arxiv.org/abs/2310.00925

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