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

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

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 $C^{\alpha, \frac{\alpha}{2}}$ regularit...

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Hauptverfasser: Attouchi, Amal, Parviainen, Mikko
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description 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 $C^{\alpha, \frac{\alpha}{2}}$ regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
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title H\"older regularity for the gradient of the inhomogeneous parabolic normalized $p$-Laplacian
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