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In this paper we study an evolution equation involving the normalized$p$-Laplacian and a bounded continuous source term. The normalized$p$-Laplacian is in non divergence form and arises for example from stochastictug-of-war games with noise. We prove local $C^{\alpha, \frac{\alpha}{2}}$regularity for the spatial gradient of the viscosity solutions. The proof isbased on an improvement of flatness and proceeds by iteration.

H\"older regularity for the gradient of the inhomogeneous parabolic normalized $p$-Laplacian