Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

@article{Camilli2019ExistenceAR,
  title={Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative},
  author={Fabio Camilli and Alessandro Goffi},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2019},
  volume={27},
  pages={1-37}
}
We study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton–Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional Hamilton–Jacobi equation obtained via nonlinear adjoint method and sharp estimates in Sobolev and Hölder spaces for the corresponding linear problem. 
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