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.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2019 8月|
ASJC Scopus subject areas