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January/February 2015 Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs
Oberman Adam M., Sviridov Alexander P., Manfredi Juan J.
Differential Integral Equations 28(1/2): 79-102 (January/February 2015).

Abstract

In this article, we study the well-posedness (uniqueness and existence of solutions) of nonlinear elliptic Partial Differential Equations (PDEs) on a finite graph. These results are obtained using the discrete comparison principle and connectivity properties of the graph. This work is in the spirit of the theory of viscosity solutions for partial differential equations. The equations include the graph Laplacian, the $p$-Laplacian, the Infinity Laplacian, and the Eikonal operator on the graph.

Citation

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Oberman Adam M.. Sviridov Alexander P.. Manfredi Juan J.. "Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs." Differential Integral Equations 28 (1/2) 79 - 102, January/February 2015.

Information

Published: January/February 2015
First available in Project Euclid: 11 December 2014

zbMATH: 1349.35382
MathSciNet: MR3299118

Subjects:
Primary: 35R02, 65N22

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 1/2 • January/February 2015
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