Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks

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.

References in corpus (4)

• A Hamilton-Jacobi approach to junction problems and application to traffic flows
• Global Results for Eikonal Hamilton-Jacobi Equations on Networks
• Shape Analysis, Lebesgue Integration and Absolute Continuity Connections
• Lax--Oleinik formula on networks

Cited by in corpus (2)

• Large Time Behavior of Solutions to Hamilton-Jacobi Equations on Networks
• Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks