R. Panenko

activity

20132025

collaborators

4 papers

math.DG2025

Some Poincaré--Sobolev inequalities for differential forms

Vladimir Gol'dshtein, Yaroslav Kopylov, Roman Panenko

We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Gol $^{'}$ dshtein and Troyanov. As in this paper, ou…

math.DG2023

On the de Rham homomorphism for $L_{π}$ -cohomologies

V. Gol'dshtein, R. Panenko

We study the procedure of regularization in the context of the Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry. It provides us with the m…

math.DG2022

A Lipschitz version of de Rham theorem for $L_{p}$ -cohomology

Vladimir Gol'dshtein, Roman Panenko

We focus our attention on the de Rham operators' underlying properties which are specified by intrinsic effects of differential geometry structures. And then we apply the procedure…

math.GR2013

$Φ$ -Harmonic Functions on Discrete Groups and First $ℓ^{Φ}$ -Cohomology

Yaroslav Kopylov, Roman Panenko

We study the first cohomology groups of a countable discrete group $G$ with coefficients in a $G$ -module $ℓ^{Φ} (G)$ , where $Φ$ is an $N$ -function of class $Δ_{2} (0) \cap \nabla_{2} (0)$ …

Some Poincaré--Sobolev inequalities for differential forms

On the de Rham homomorphism for Lπ​-cohomologies

A Lipschitz version of de Rham theorem for Lp​-cohomology

Φ-Harmonic Functions on Discrete Groups and First ℓΦ-Cohomology

On the de Rham homomorphism for $L_{π}$ -cohomologies

A Lipschitz version of de Rham theorem for $L_{p}$ -cohomology

$Φ$ -Harmonic Functions on Discrete Groups and First $ℓ^{Φ}$ -Cohomology