On the Dirichlet and Neumann Evolution Operators in ℝ d+ R _+

摘要: We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators and associated with a class of nonautonomous elliptic operators (t) with unbounded coefficients defined in I× (where I is a right-halfline or I=ℝ). We also prove the existence and the uniqueness of a tight evolution system of measures associated with , which turns out to be sub-invariant for , and we study the asymptotic behaviour of the evolution operators and in the L p -spaces related to the system .