H\"older estimates for viscosity solutions of equations of fractional $p$-Laplace type

We prove H"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$\text{PV}{\int }_{{\mathbb{R}}^n}\frac{\mathrm{\mid }u(x)-u(x+y){\mathrm{\mid }}^{p-2}(u(x)-u(x+y))}{\mathrm{\mid }y{\mathrm{\mid }}^{n+sp}}dy=0,$$ where $s\in (0,1)$ and $p>2$ or $1\mathrm{/}(1-s)<p<2$. Our results also apply for inhomogeneous equations with more general kernels, when $p$ and $s$ are allowed to vary with $x$, without any regularity assumption on $p$ and $s$. This complements and extends some of the recently obtained H"older estimates for weak solutions.