On the solvability of the Dirichlet problem for anisotropic parabolic equations in non-convex domains

The Cauchy—Dirichlet problem in non-convex domains for anisotropic parabolic equation with time-dependent exponents and gradient term is considered. We state sufficient conditions that guarantee the existence and uniqueness of a viscosity solution which is Lipschitz continuous in the space variables and Hölder continuous in time.