Generalized and classical maximum principle for class of second order elliptic systems

Abstract EN

In this paper we find a generalized maximum principle for weakly coupled second order homogeneous elliptic systems Lu + Au = 0 in ? ? Rn Where L [u(x)]= aij(x) + ai (x) , aij = aji is a second order real elliptic operator, u=(u1, u2, …, un)T, and A is an n ? n matrix with entries which are all complex valued functions.

We also find a sufficient condition for the classical maximum principle.

These results extend the result of Winter and Wong [12] for A being negative semidefinite to a more general form of A.

Generalized maximum principles for weakly coupled second order elliptic systems have also been obtained by Dow [2], Hile and Protter [6], and Wasowski [11] under different conditions on the coefficients.