On weakly coupled systems of partial differential equations with different diffusion terms

摘要: We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space of bounded and continuous functions, associated to a class of nonautonomous weakly coupled second-order elliptic operators , with possibly unbounded coefficients and diffusion and drift terms which vary from equation to equation. We also provide estimates of the spatial derivatives up to the third-order and continuity properties both of the evolution operator associated to the Cauchy problem in , and, for fixed , of the semigroup associated to the autonomous Cauchy problem in . These results allow us to deal with elliptic problems whose coefficients also depend on time.