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arXiv · 2603.16168

Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games

Mikhail Gomoyunov
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Abstract

We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary condition. Under assumptions on the Hamiltonian that are more general than those previously considered in the literature and allow, in particular, a measurable dependence on the first (time) variable, we establish existence, uniqueness, stability, and consistency results for minimax solutions. As an application, we consider a zero-sum differential game for a time-delay system and prove that this game has a value under assumptions more general than the known ones but rather natural being consistent with the Carath\'{e}odory conditions.

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Mikhail Gomoyunov. 2026-03-17. Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games. https://arxiv.org/abs/2603.16168

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