The weak Harnack inequality for Lp-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 Lp-viscosity solutions is derived from the weak Harnack inequality for Lp-viscosity supersolutions. The local maximum principle for Lp-viscosity subsolutions and the Harnack inequality for Lp-viscosity solutions are also obtained. Several further remarks are presented when equations have superlinear growth in the first space derivatives.
MSC Codes 49L25, 35D40, 35B65, 35K55, 35K20, 35K10
|Publication status||Published - 2018 Nov 19|
- Fully nonlinear parabolic equations
- Harnack inequality
- Maximum principle
- Viscosity solutions
ASJC Scopus subject areas