Maximum principle and existence of solutions for systems involving \(\text{div}(\rho\nabla)U\) operator on a bounded domain (Q2566843)

Let \(\Omega \) be a smooth bounded domain in \(\mathbb R^N\). The paper deals with the Dirichlet problem for the system \(\sum \partial_j (\rho_i \partial_j u_i )=\sum a_{ij}u_j +f_i \) in \(\Omega \), \(u_i =0\) on \(\partial \Omega \), \(1\leq i\leq n\). Under certain conditions the maximum principle for this system and the existence and the uniqueness of a solution of the Dirichlet problem is proved.