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arXiv · 2412.01625

Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks

Marco Pozza
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Abstract

We extend the study of eikonal Hamilton-Jacobi equations posed on networks performed by Siconolfi and Sorrentino (Anal. PDE, 2018) to a more general setting. Their approach essentially exploits that such equations correspond to discrete problems on an abstract underlying graph. However, a specific condition they assume can be rather restricting in some settings, which motivates the generalization we propose. We still get an Aubry set, which plays the role of a uniqueness set for our problem and appears in the representation of solutions. Exploiting it we establish a new comparison principle between super and subsolutions to the equation.

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Marco Pozza. 2024-12-02. Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks. https://doi.org/10.3934/dcds.2025071

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