I have been reading a paper, on monge-ampere type equations, and the existence of a unique convex solution has been proven to exist in $C^{3,\alpha}(\Omega)\cap C^{2,\alpha}(\overline{\Omega})$, for any $\alpha\in(0,1)$, where $\Omega$ is a convex domain.
I believe these sets $C^{3,\alpha}$ are something to do with the cone of convex functions, but I cannot find anywhere that explains the notation, and what such sets these are, so any help would be greatly apprectiated.
Usually, $C^{k,\alpha}$ denotes the set of $k$-times differentiable functions, whose $k$th derivative is Hölder-continuous with exponent $\alpha$.