On the initial time behavior of spatial derivatives for solutions of the parabolic Cauchy problem (Q1373437)

The author considers the parabolic Cauchy problem \[ {\partial u\over \partial t}= \sum^n_{j,k=1} a_{jk}(x,t) {\partial^2u \over\partial x_j \partial x_k}+ \sum^N_{j=1} b_j(x,t) {\partial u\over \partial x_j} +c(x,t)u \quad\text{ in } \mathbb{R}^n \times(0,T);\;u(x,0) =f(x). \] The continuity of the spatial derivatives for solutions is established down to the initial time under the assumption that the initial data and coefficients are sufficiently smooth.