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

Abstract

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

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Nov 19

Keywords

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

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications'. Together they form a unique fingerprint.

Cite this