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

Amal Attouchi; Mikko Parviainen

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arXiv · 1610.04987

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

Amal Attouchi·Mikko Parviainen

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Abstract

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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Amal Attouchi, Mikko Parviainen. 2016-10-17. H\"older regularity for the gradient of the inhomogeneous parabolic normalized $p$-Laplacian. https://arxiv.org/abs/1610.04987

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