Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces

Fabian Fuchs

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arXiv · 2610.18496

Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces

Fabian Fuchs

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Abstract

This work provides a framework to treat optimal control problems on separable Banach spaces in the viscosity sense. First, it extends the notion of $B$-viscosity solutions to the Banach setting and relates the extension to the notions of viscosity solutions used in metric space settings. As the main results, the paper proves a strict comparison principle and characterizes the value function of an optimal control problem as the unique viscosity solution to an infinite-dimensional HJB equation.

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BibTeX RIS

Fabian Fuchs. 2026-10-13. Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces. https://arxiv.org/abs/2610.18496

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