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October 2021 Some function theoretic properties of nonlinear resistive networks
Tae HATTORI, Atsushi KASUE, Motoki OHKUBO
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Hokkaido Math. J. 50(3): 409-454 (October 2021). DOI: 10.14492/hokmj/2019-196

Abstract

We consider nonlinear resistive networks. The equivalence of the Liouville property, the Khas'minskii condition and the weak maximum principle for operators of Laplacian with potential is proved, and a number of criteria for these properties are given. The parabolicity of networks is also discussed.

Funding Statement

The second author is partially supported by the Grant-In-Aid for Scientific Research (C) 16K05124 and Scientific Research (A) 17H01092 of the Japan Society for the Promotion of Science.

Acknowledgment

We would like to thank the referee for careful readings of the manuscript and valuable comments that improved the exposition.

Citation

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Tae HATTORI. Atsushi KASUE. Motoki OHKUBO. "Some function theoretic properties of nonlinear resistive networks." Hokkaido Math. J. 50 (3) 409 - 454, October 2021. https://doi.org/10.14492/hokmj/2019-196

Information

Received: 27 October 2019; Revised: 31 July 2020; Published: October 2021
First available in Project Euclid: 17 December 2021

Digital Object Identifier: 10.14492/hokmj/2019-196

Subjects:
Primary: 05C63 , 31C20

Keywords: Khas'minskii condition , Laplace operator , Liouville property , nonlinear network , parabolicity , weak maximum principle

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 3 • October 2021
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