Interior continuity, continuity up to the boundary and Harnack's inequality for double-phase elliptic equations with non-logarithmic conditions

Oleksandr V. Hadzhy, Igor I. Skrypnik, Mykhailo V. Voitovych

We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type $$ \begin{aligned} {\rm div}\big(|\nabla u|^{p-2}\,\nabla u+a(x)|\nabla u|^{q-2…