THE MAXIMUM MODULUS PRINCIPLE FOR A CLASS OF ELLIPTIC SYSTEMS OF DIFFERENTIAL EQUATIONS.

In the paper, sufficiently wide classes of systems of elliptic differential equations are studied from the view of the maximum modulus principle. The classes of corresponding systems of equations are constructively described, for which the maximum modulus principle is valid in the classical version and it is argued that beyond these classes, in general, the maximum modulus principle is violated in the mentioned form. With the obtained results, in particular, the problem posed by B. Bojarski in [13] is partially solved. [ABSTRACT FROM AUTHOR]