Abstract
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.
Original language | English |
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Pages (from-to) | 264-289 |
Number of pages | 26 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 185 |
DOIs | |
Publication status | Published - 2019 Aug |
Externally published | Yes |
Keywords
- Fully nonlinear parabolic equations
- Harnack inequality
- Maximum principle
- Viscosity solutions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics