Maximum principle in some unbounded domains for an elliptic operator with unbounded drift

We study the maximum principle for (wG)-domain, which can be unbounded. The (wG)-condition was introduced by A. Vitolo and the maximum principle was proved for the uniformly elliptic operator with bounded coefficients. Using Safonov's growth lemma, we treat the operator when the first order coefficients belong to n-integrable Lebesgue space. Some examples including infinite cones, various unbounded coefficients, are presented.