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

摘要

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 Holder 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. (C) 2019 Elsevier Ltd. All rights reserved.