Generation results for vector-valued elliptic operators with unbounded coefficients in Lp spaces

We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first-order, in the Lebesgue space Lp(Rd;Rm). Sufficient conditions to prove generation results of an analytic C0-semigroup T (t), together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established