Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition (Q6113265)

In this paper, the authors study a class of parabolic equations with nonstandard growth conditions. More precisely they consider the degenerate parabolic equations with \((p,q)\) growth \[ u_t-\Delta_pu+ a(x, t) \Delta_qu = 0, \,\, a(x, t)\geq 0, \] under the generalized non-logarithmic Zhikov's conditions. They prove intrinsic Harnack-type inequalities for bounded non-negative solutions. This structural property is basically characterized by various types of degenerate behavior, according to the size of the coefficient \(a(x, t)\) that determines the phase.