Maximum principles for elliptic systems (Q1176583)

A generalized maximum principle is established for a weakly coupled second-order elliptic system of the type \(Lu+Cu=0\) in \(D\subset\mathbb{R}^ n\), where \(L\) is a second order real elliptic operator and the matrix \(C=C(x)\) is such that \(C^*(x)B+BC(x)\leq 0\) in \(D\), where \(B>0\) is a complex constant matrix. A reduction to Lyapunov's second method is used in obtaining the maximum principle.