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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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Cite

BibTeXRIS
BibTeX
@misc{fuchs2026viscosity,
  title = {{Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces}},
  author = {Fabian Fuchs},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18496},
  eprint = {2610.18496},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18496},
}
RIS
TY  - UNPB
TI  - Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces
AU  - Fabian Fuchs
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18496
UR  - https://arxiv.org/abs/2610.18496
AB  - 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.
ER  -