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

 Koike Shigeaki KOIKE Shigeaki
 Department of Mathematics Saitama University

 Swiech Andrzej SWIECH Andrzej
 School of Mathematics Georgia Institute of Technology
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Author(s)

 Koike Shigeaki KOIKE Shigeaki
 Department of Mathematics Saitama University

 Swiech Andrzej SWIECH Andrzej
 School of Mathematics Georgia Institute of Technology
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 AleksandrovBakelmanPucci maximum principle in unbounded domains.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 61(3), 723755, 20090701
The Mathematical Society of Japan
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