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ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms

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Abstract

Aleksandrov–Bakelman–Pucci maximum principles are studied for a class of fully nonlinear integro-differential equations of order \(\sigma \in [2-\varepsilon _0,2)\), where \(\varepsilon _0\) is a small constant depending only on given parameters. The goal of this paper is to improve an estimate of Guillen and Schwab (Arch Ration Mech Anal 206(1):111–157, 2012) in order to avoid the dependence on \(L^\infty\) norm of the inhomogeneous term.

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Acknowledgements

The author wishes to express his thanks to Prof. Shigeaki Koike for many stimulating conversations and careful reading of the first draft.

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Authors and Affiliations

  1. Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

    Shuhei Kitano

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  1. Shuhei Kitano
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Correspondence to Shuhei Kitano.

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This article is part of the topical collection “Viscosity solutions -- Dedicated to Hitoshi Ishii on the award of the 1st Kodaira Kunihiko Prize” edited by Kazuhiro Ishige, Shigeaki Koike, Tohru Ozawa and Senjo Shimizu.

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Kitano, S. ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms. SN Partial Differ. Equ. Appl. 1, 16 (2020). https://doi.org/10.1007/s42985-020-00018-y

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  • DOI: https://doi.org/10.1007/s42985-020-00018-y

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