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

Shigeaki Koike*, Andrzej Świȩch

*この研究の対応する著者

研究成果: Article査読

30 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)723-755
ページ数33
ジャーナルJournal of the Mathematical Society of Japan
61
3
DOI
出版ステータスPublished - 2009 7月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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