Maximum principles for elliptic dynamic equations

We consider second-order partial dynamic operators of the elliptic type on time scales. We establish basic maximum principles and apply them to obtain the uniqueness of Dirichlet boundary value problems for dynamic elliptic equations, e.g. Poisson equation. Our special cases include the situation in which several variables are continuous and the others discrete. We conclude with open problems; we discuss the role of regressive groups in more dimensions.