The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

Abstract

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak–Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a suitable Lebesgue or Sobolev space. Furthermore, we establish the sharpness of our central assumptions.