Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs
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.
Fields of Study & Subjects
Middle East Politics and Society
Nonlinear Partial Differential Equations
Graph theory and applications
Publication details
- Journal / source
- Journal de l’École polytechnique — Mathématiques
- Publisher
- MathDoc/Centre Mersenne
- Volume
- 13
- Pages
- 965–1005
- Publication date
- 19 May 2026
- Language
- EN