Differential and Integral Equations

Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs

Oberman Adam M., Sviridov Alexander P., and Manfredi Juan J.

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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.

Article information

Differential Integral Equations, Volume 28, Number 1/2 (2015), 79-102.

First available in Project Euclid: 11 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R02: Partial differential equations on graphs and networks (ramified or polygonal spaces) 65N22: Solution of discretized equations [See also 65Fxx, 65Hxx]


Juan J., Manfredi; Adam M., Oberman; Alexander P., Sviridov. Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs. Differential Integral Equations 28 (2015), no. 1/2, 79--102. https://projecteuclid.org/euclid.die/1418310422

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