  A new method to compute Schauder Estimates for multidimensional fourth order
heat-type equations is proposed. In particular, we show how knowing Schauder or
Sobolev estimates for the one-dimensional fourth order heat equation allows to
derive their multidimensional analogs for equations with time inhomogeneous
coefficients with the same constants as in the case of the one-dimensional heat
equation. Our method relies on a merger between (Krylov and Priola, 2017),
where they actually showed the same result for the classical second order heat
equation and (Funaki, 1979), where a probabilistic construction of solutions
for the fourth order heat equation is presented.
