Calculus of Variations and Geometric Measure Theory
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F. Camilli - A. Goffi

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

created by goffi on 01 Jul 2019
modified on 13 Mar 2020


Published Paper

Inserted: 1 jul 2019
Last Updated: 13 mar 2020

Journal: NoDEA
Pages: 30
Year: 2019
Doi: 10.1007/s00030-020-0624-0

ArXiv: 1906.01338 PDF


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


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