Regularity theory for fully nonlinear equations of porous medium-type

In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global C2,α-estimates of viscosity solutions. In many PDE problems, the C2,α-estimates have been obtained through Schauder-type estimates. However, the Schauder-type estimates are not applicable to the porous medium-type equations. We provide techniques for handling porous medium-type equations so that the global C2,α-estimates can be established.