Archivio Istituzionale della RicercaEvery graph of bounded degree endowed with the counting measure satisfies a local version of L-p-Poincare inequality, p is an element of [1, infinity]. We show that on graphs which are trees the Poincare constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of L-p-Poincare inequality, despite the fact that they are nondoubling measures of exponential growth.
Poincaré inequalities on graphs / Levi, M.; Santagati, F.; Tabacco, A.; Vallarino, M.. - In: ANALYSIS MATHEMATICA. - ISSN 0133-3852. - 49:2(2023), pp. 529-544. [10.1007/s10476-023-0215-5]
Poincaré inequalities on graphs
Santagati F.;Tabacco A.;Vallarino M.
2023
Abstract
Every graph of bounded degree endowed with the counting measure satisfies a local version of L-p-Poincare inequality, p is an element of [1, infinity]. We show that on graphs which are trees the Poincare constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of L-p-Poincare inequality, despite the fact that they are nondoubling measures of exponential growth.
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https://hdl.handle.net/11583/2982605