Γ-convergence and homogenisation for a class of degenerate functionals. (January 2020)

• Record Type: Journal Article
• Authors: Dirr, Nicolas; Dragoni, Federica; Mannucci, Paola; Marchi, Claudio
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: Gamma-convergence -- Homogenisation -- Carnot groups -- Heisenberg group -- Hörmander condition -- Degenerate functionals; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111618
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is on Γ -convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the geometry of the Heisenberg group. Without using special geometric features, these functionals would be neither coercive nor periodic, so classic results do not apply. All the results apply to the more general case of Carnot groups.