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We consider a class of vector-valued elliptic operators with unboundedcoefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m)with p in (1,\infty). Sufficient conditions to prove generation results of ananalytic C_0-semigroup T(t), together with a characterization of the domain ofits generator, are given. Some results related to the hypercontractivity andthe ultraboundedness of the semigroup are also established.

Generation results for vector-valued elliptic operators with unbounded coefficients in L^p spaces