Φ-ГАРМОНИЧЕСКИЕ ФУНКЦИИ НА ГРАФАХ

Roman Panenko

doi:10.17377/semi.2017.14.001

Φ-ГАРМОНИЧЕСКИЕ ФУНКЦИИ НА ГРАФАХ

Translated title of the contribution: Φ-harmonic functions on graphs

Roman Panenko

Research output: Contribution to journal › Article › peer-review

Abstract

We study certain problems of Φ-harmonic analysis on graphs, where Φ is a strictly convex N-function.We introduce the key definitions and reveal that the ones in question are well-defined and what basic properties of harmonic functions hold. Also we prove discrete analogs of classical theorems for harmonic function in the usual sense: uniqueness theorem, Harnack's inequality, Harnack's principle etc.

Translated title of the contribution	Φ-harmonic functions on graphs
Original language	Russian
Pages (from-to)	1-9
Number of pages	9
Journal	Siberian Electronic Mathematical Reports
Volume	14
DOIs	https://doi.org/10.17377/semi.2017.14.001
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

Graph
Harnack's inequality
N-function
Φ-harmonicity

ASJC Scopus subject areas

General Mathematics

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10.17377/semi.2017.14.001

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abstract = "We study certain problems of Φ-harmonic analysis on graphs, where Φ is a strictly convex N-function.We introduce the key definitions and reveal that the ones in question are well-defined and what basic properties of harmonic functions hold. Also we prove discrete analogs of classical theorems for harmonic function in the usual sense: uniqueness theorem, Harnack's inequality, Harnack's principle etc.",

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AB - We study certain problems of Φ-harmonic analysis on graphs, where Φ is a strictly convex N-function.We introduce the key definitions and reveal that the ones in question are well-defined and what basic properties of harmonic functions hold. Also we prove discrete analogs of classical theorems for harmonic function in the usual sense: uniqueness theorem, Harnack's inequality, Harnack's principle etc.

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KW - Harnack's inequality

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KW - Φ-harmonicity

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Φ-ГАРМОНИЧЕСКИЕ ФУНКЦИИ НА ГРАФАХ

Abstract

Keywords

ASJC Scopus subject areas

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