Hölder gradient estimates for parabolic homogeneous p-Laplacian equations

Abstract: We prove interior H\"older estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous $p$-Laplacian equation [ u_t=|\nabla u|^{2-p} \mbox{ div} (|\nabla u|^{p-2}\nabla u), ] where $1<p<\infty$. This equation arises from tug-of-war-like stochastic games with noise. It can also be considered as the parabolic $p$-Laplacian equation in non divergence form.