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

The weak Harnack inequality for L ^p -viscosity supersolutions of fully nonlinear second-order uniformly parabolic partial differential equations with unbounded coefficients and inhomogeneous terms is proved. It is shown that Hölder continuity of L ^p -viscosity solutions is derived from the weak Harnack inequality for L ^p -viscosity supersolutions. The local maximum principle for L ^p -viscosity subsolutions and the Harnack inequality for L ^p -viscosity solutions are also obtained. Several further remarks are presented when equations have superlinear growth in the first space derivatives.