Two-scale homogenization in the Heisenberg group
type: Item
instance of: scholarly article
title: Two-scale homogenization in the Heisenberg group
zbMATH Open document ID: 1031.35019
DOI: 10.1016/S0021-7824(01)01247-8
author: Bruno Franchi
author: Maria Carla Tesi
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2003-09-07T00:00:00Z
review text: The authors consider a problem of periodic homogenization with respect to the Heisenberg group (the periodicity is defined by group translations and the intrinsic anisotropic dilations of the group). The problem considered is relative to a generalized Cohn-Laplacian with strongly oscillating (Heisenberg-) periodic coefficients in a domain perforated with interconnected (Heisenberg-) periodic pipeline. The convergence to a precisely described homogeneized problem is obtained by the two-scale method in a version adapted to the geometry of the group.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 43A80
zbMATH DE Number: 1975943
zbMATH Keywords: two-scale convergence
zbMATH Keywords: periodic coefficients
zbMATH Keywords: intrinsic anisotropic dilations of the group
MaRDI profile type: Publication
cites work: Homogenization and Two-Scale Convergence
cites work: Q4308154
cites work: Q4879951
cites work: Q4364829
cites work: Homogenization for Heisenberg operator with Neumann boundary conditions
cites work: Q3836478
cites work: Q5565773
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
cites work: Rectifiability and perimeter in the Heisenberg group
cites work: Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces
cites work: Finite element approximation of the Navier-Stokes equations. Rev. repr. of the 1st ed
cites work: Q4040640
cites work: Hypoelliptic second order differential equations
cites work: The Poincaré inequality for vector fields satisfying Hörmander's condition
cites work: Regular domains in homogeneous groups
cites work: Surface measures in Carnot-Carathéodory spaces
cites work: A General Convergence Result for a Functional Related to the Theory of Homogenization
cites work: Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
cites work: On the nonexistence of bilipschitz parameterizations and geometric problems about \(A_ \infty\)-weights
cites work: Q3142876
cites work: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
cites work: Connectedness and homogenization. Examples of fractal conductivity
full work available at URL: s0021-7824(01)01247-8
OpenAlex ID: W2049216403
Recommended article: Homogenization and Two-Scale Convergence
Recommended article: Q4364829
Recommended article: Homogenization of Hamilton-Jacobi equations in the Heisenberg group
Recommended article: Q4380814
Recommended article: Homogenization Estimates for Singularly Perturbed Operators
Recommended article: Two-scale homogenization of non-linear degenerate evolution equations
Recommended article: Homogenization of two-phase metrics and applications
Recommended article: Q4308154
Recommended article: Two‐scale cut‐and‐projection convergence; homogenization of quasiperiodic structures
Recommended article: Homogenization and two-scale convergence in the Sobolev space with an oscillating exponent
description: scientific article; zbMATH DE number 1975943