Maximum principle for higher order operators in general domains

Abstract We first prove De Giorgi type level estimates for functions in W 1, t (Ω), Ω ⊂ mathvariant="double-struck">R N $ \Omega\subset{\mathbb R}^N , with t > ≥ 2 \gt N\geq 2 . This augmented integrability enables us to establish a new Harnack inequality which do not necessarily belong Giorgi’s classes as obtained Di Benedetto–Trudinger [10] 1,2 (Ω). As consequence, we the validity of strong maximum principle uniformly elliptic operators any even order, fairly general domains dimension two and three, provided second order derivatives are taken into account.