Hölder continuity of parabolic quasi-minimizers

We are concerned with scalar valued local parabolic quasi-minimizers u associated to a Carathéodory integrand f obeying p-growth assumptions for p>1. For such parabolic quasi-minimizers we prove local Hölder continuity provided they are already locally bounded. The superquadratic case p≥2 has already been considered in [17], [22], whereas the subquadratic case could, at least to our knowledge, not be treated in the past. In this paper we are able to handle both the sub- and superquadratic case under more general growth conditions.