Authors

Kazufumi Ito

Abstract

In this paper we show the existence of solutions with quadratic growth to Hamilton–Jacobi–Bellman equations. We assume that the Hamiltonian has the quadratic growth both in x and p. We obtain the explicit Lipschitz bound of solutions in the weighted sup-norm. Also, we discuss the vanishing viscosity limit of solutions and show the existence of viscosity solutions to the resulting Hamilton–Jacobi equation.

Citation

  • Journal: Journal of Differential Equations
  • Year: 2001
  • Volume: 176
  • Issue: 1
  • Pages: 1–28
  • Publisher: Elsevier BV
  • DOI: 10.1006/jdeq.2000.3980

BibTeX

@article{Ito_2001,
  title={{Existence of Solutions to the Hamilton–Jacobi–Bellman Equation under Quadratic Growth Conditions}},
  volume={176},
  ISSN={0022-0396},
  DOI={10.1006/jdeq.2000.3980},
  number={1},
  journal={Journal of Differential Equations},
  publisher={Elsevier BV},
  author={Ito, Kazufumi},
  year={2001},
  pages={1--28}
}

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