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arXiv · 2303.04629

A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications

Fabio Camilli·Claudio Marchi
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Abstract

We study continuous dependence estimates for viscous Hamilton- Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C2-norm of the difference between the corresponding solutions in terms of the distance among the coefficients. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result for a quasi-stationary Mean Field Games defined on the network Gamma; the second one is an estimate of the rate of convergence for homogenization of Hamilton-Jacobi equations defined on a periodic network, when the size of the cells vanishes and the limit problem is defined in the whole Euclidean space.

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Fabio Camilli, Claudio Marchi. 2023-03-08. A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications. https://arxiv.org/abs/2303.04629

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