On differentiability preserving properties of semigroups associated with one-dimensional singular diffusions (Q1057002)

The author considers a one-dimensional diffusion on a finite interval. He shows that if the coefficient in the second derivative of the generator is not differentiable at boundary points then the semigroup of transition operators may not preserve the three-times differentiability of the initial data. Still, for sufficiently many initial data the one and two- times differentiability preserving properties hold true.