Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficients

Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient the square root a differentiable function but not itself. For every $m\in\{0,1,2\}$ establish an upper bound $C^m$-norm semigroup such in terms $C^m$-norms drift and squared coefficient. The constants our are often dimension-independent. Our estimates thus suitable analyzing certain high-dimensional infinite-dimensional degenerate equations.