Local boundedness for solutions to parabolic double phase problems

Source abstract

In this paper, we investigate the local boundedness of weak solutions to parabolic double phase equations of type [Formula: see text] where [Formula: see text] and [Formula: see text], so that both the degenerate range [Formula: see text] and the singular range [Formula: see text] are covered. To this end, we derive the Caccioppoli inequality and recall a parabolic embedding theorem, which are then utilized in an iteration method.