Weak Harnack inequality for fully nonlinear uniformly elliptic pde with unbounded ingredients

Shigeaki Koike, Andrzej Świȩch

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23 Citations (Scopus)


The weak Harnack inequality for Lp-viscosity solutions is shown for fully nonlinear, second order uniformly elliptic partial differential equations with unbounded coefficients and inhomogeneous terms. This result extends those of Trudinger for strong solutions [21] and Fok for L p-viscosity solutions [13]. The proof is a modification of that of Caffarelli [5], [6], We apply the weak Harnack inequality to obtain the strong maximum principle, boundary weak Harnack inequality, global Cα estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.

Original languageEnglish
Pages (from-to)723-755
Number of pages33
JournalJournal of the Mathematical Society of Japan
Issue number3
Publication statusPublished - 2009 Jul 1



  • Lviscosity solution
  • Weak Harnack inequality

ASJC Scopus subject areas

  • Mathematics(all)

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