Hölder regularity for non-autonomous abstract parabolic equations

This paper contains some existence and uniqueness results for the strict and classical solutionsu : 0,T] →E of the non-autonomous evolution equationu ¹(t)=Λ(t)u(t)+f(t) in a Banach spaceE under the classical Tanabe-Sobolevski assumptions. These results do not require use of the fundamental solution and give new information about the hölder-regularity of the solutions.