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

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Author(s)

Abstract

The weak Harnack inequality for <I>L<SUP>p</SUP></I>-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 <I>L<SUP>p</SUP></I>-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 <I>C</I><SUP>α</SUP> estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 61(3), 723-755, 2009-07-01

    The Mathematical Society of Japan

References:  20

Cited by:  1

Codes

  • NII Article ID (NAID)
    10026998426
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    Journal Article
  • ISSN
    00255645
  • NDL Article ID
    10286787
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  CJPref  NDL  J-STAGE 
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