# 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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