Work

Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs

Year: 2026

Type: article

Abstract: We investigate the equivalence of Sobolev inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the normalizing measure, we obtain the equivalence up to constants. If arbitrary measures are considered, we incorporate a new local regularity condition. Furthermore, new correction functions for the Gaussian, doubling, and Sobolev dimension are introduced. For the Gaussian and doubling, the variable correction functions always tend to one at infinity. Moreover, the variable Sobolev dimension can be related to the doubling dimension and the vertex degree growth.

Source: Journal de l’École polytechnique — Mathématiques

DOI: 10.5802/jep.340

Authors: Matthias Keller, Christian Rose

Institution: University of Potsdam

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

OpenAlex ID: W4400221741