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Improved regularity for a time-dependent Isaacs equation

Giane Casari Rampasso

The purpose of this work is to discuss a regularity theory for viscosity solutions to a parabolic problem driven by the Isaacs operator. Under distinct smallness regime imposed on the coefficients, our findings are three-fold; first, we produce estimates in Sobolev spaces. It includes operators with dependence on the gradient. Then we examine the regularity in Hölder spaces. Here we deal with the boderline case and, if we refine the smallness regime, estimates in $\mathcal{C}^{2+\gamma,\frac{2+\gamma}{2}}$ are produced. This is done through geometric and approximation techniques with preliminary compactness and localization arguments.