Work

The Liouville Theorem for Discrete Symmetric Averaging Operators

Year: 2024

Type: article

Abstract: We introduce averaging operators on lattices $$\mathbb Z^d$$ Z d and study the Liouville property for functions satisfying mean value properties associated to such operators. This framework encloses discrete harmonic, p-harmonic, $$\infty $$ ∞ -harmonic and the so-called game p-harmonic functions. Our approach provides an elementary alternative proof of the Liouville Theorem for positive p-harmonic functions on $$\mathbb Z^d$$ Z d .

Source: Potential Analysis

DOI: 10.1007/s11118-024-10174-0

Authors: Tomasz Adamowicz, José G. Llorente

Institutions: Institute of Mathematics, Polish Academy of Sciences, Universidad Complutense de Madrid

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Ministerio de Economía y Competitividad, Narodowe Centrum Nauki, Ministerstwo Edukacji i Nauki, Instytut Matematyczny, Polskiej Akademii Nauk