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The weak Harnack inequality for $L^p$-viscosity supersolutions of fullynonlinear second-order uniformly parabolic partial differential equations withunbounded coefficients and inhomogeneous terms is proved. It is shown thatH\"older continuity of $L^p$-viscosity solutions is derived from the weakHarnack inequality for $L^p$-viscosity supersolutions. The local maximumprinciple for $L^p$-viscosity subsolutions and the Harnack inequality for$L^p$-viscosity solutions are also obtained. Several further remarks arepresented when equations have superlinear growth in the first spacederivatives.

Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications