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July, 2009 Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients
Shigeaki KOIKE, Andrzej ŚWIĘCH
J. Math. Soc. Japan 61(3): 723-755 (July, 2009). DOI: 10.2969/jmsj/06130723

Abstract

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

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Shigeaki KOIKE. Andrzej ŚWIĘCH. "Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients." J. Math. Soc. Japan 61 (3) 723 - 755, July, 2009. https://doi.org/10.2969/jmsj/06130723

Information

Published: July, 2009
First available in Project Euclid: 30 July 2009

zbMATH: 1228.35104
MathSciNet: MR2552914
Digital Object Identifier: 10.2969/jmsj/06130723

Subjects:
Primary: 35J60, 49L25

Rights: Copyright © 2009 Mathematical Society of Japan

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Vol.61 • No. 3 • July, 2009
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