Holder Regularity for the Linearized Porous Medium Equation in Bounded Domains

In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized porous medium equation with the homogeneous Dirichlet boundary condition.We prove the H ölder regularity of their weak solutions.