# 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}
}
• Published 4 June 2019
• Mathematics
• Nonlinear Differential Equations and Applications NoDEA
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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