Local boundedness for solutions to degenerate parabolic double phase problems

Abstract

In this paper, we investigate the local boundedness of weak solutions to degenerate parabolic double phase equation of type $$u_t-\text{div}(|Du{|}^{p-2}Du+a(x,t)|Du{|}^{q-2}Du)=0\text{in }\hat{I}{\text{c◯}}_T:=\hat{I}\text{c◯}\times (0,T),$$ where $0\le a(\cdot )\in L^{\infty }(\hat{I}{\text{c◯}}_T)$. To this end, we derive the Caccioppoli inequality and a parabolic embedding theorem, which are then utilized in an iteration method.