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

Shigeaki Koike, Andrzej Święch, Shota Tateyama

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)264-289
Number of pages26
JournalNonlinear Analysis, Theory, Methods and Applications
Volume185
DOIs
Publication statusPublished - 2019 Aug

Keywords

  • Fully nonlinear parabolic equations
  • Harnack inequality
  • Maximum principle
  • Viscosity solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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