Inserted: 1 jul 2019
Last Updated: 13 mar 2020
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 H\"older spaces for the corresponding linear problem.
Keywords: adjoint method, time-fractional Hamilton-Jacobi equations, Caputo derivative, Schauder estimate