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We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p-Laplacian type and in non-divergence form. We provide local Hölder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Hölder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

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 stochastic tug-of-war games with noise. We prove local C α, α 2 regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.Recently, a connection between the theory of stochastic tug-of-war games and non-linear equations of p-Laplacian type has been investigated. In the elliptic case, this connection started with the seminal

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