Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation

Abstract

We consider interior Hölder regularity of the spatial gradient of viscosity solutions to the normalized $p(x,t)$-Laplace equation $$u_t=\left({\delta }_{ij}+(p(x,t)-2)\frac{u_i{u}_j}{|Du{|}^2}\right)u_{ij}$$ with some suitable assumptions on $p(x,t)$, which arises naturally from a two-player zero-sum stochastic differential game with probabilities depending on space and time.

References in corpus (1)

• Tug-of-war and the infinity Laplacian