\(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization

DOI10.1515/acv-2015-0053zbMath1391.49019arXiv1511.09296OpenAlexW2964067321MaRDI QIDQ2409046

Jean-Philippe Mandallena, Omar Anza Hafsa

Publication date: 10 October 2017

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.09296

zbMATH Keywords

homogenizationrelaxation\(\Gamma\)-convergencemetric measure spaceCheeger-Sobolev spacenonconvex integral

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for problems in abstract spaces (49J27)

Related Items (9)

Stochastic homogenization of nonconvex integrals in the space of functions of bounded deformation ⋮ $\Gamma$-Convergence for Functionals Depending on Vector Fields. II. Convergence of Minimizers ⋮ Mass Optimization Problem with Convex Cost ⋮ A note on BV and 1-Sobolev functions on the weighted Euclidean space ⋮ High Contrasting Diffusion in Heisenberg Group: Homogenization of Optimal Control via Unfolding ⋮ \( \Gamma \)-convergence and homogenisation for a class of degenerate functionals ⋮ On subadditive theorems for group actions and homogenization ⋮ Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces ⋮ Integral representation and relaxation of local functionals on Cheeger-Sobolev spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the relaxation of variational integrals in metric Sobolev spaces
• Nonlinear potential theory on metric spaces
• Global-local subadditive ergodic theorems and application to homogenization in elasticity.
• Non convex homogenization problems for singular structures
• Homogenization of nonconvex integral functionals and cellular elastic materials
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• An introduction to \(\Gamma\)-convergence
• Axiomatic theory of Sobolev spaces
• Second-order energies on thin structures: Variational theory and non-local effects
• Interchange of infimum and integral
• Averaging of problems in the theory of elasticity on singular structures.
• \(L^q\)-differentials for weighted Sobolev spaces
• On the relaxation of nonconvex superficial integral functionals
• Definitions of Sobolev classes on metric spaces
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Homogenization of second order energies on periodic thin structures
• Differentiability of \(p\)-harmonic functions on metric measure spaces
• Quasiconvexification of geometric integrals
• Relaxation and integral representation for functionals of linear growth on metric measure spaces
• Energies with respect to a measure and applications to low dimensional structures
• Homogenization of Thin Structures by Two-Scale Method with Respect to Measures
• $\Gamma$-limits of functionals determined by their infima
• Nonsmooth calculus
• Ergodic theorems for superadditive processes.
• Ergodic theorems for spatial processes
• Liouville theorems for harmonic sections and applications
• Lower semicontinuity of multiple µ-quasiconvex integrals
• Sobolev met Poincaré
• Homogenization of elasticity problems on singular structures

This page was built for publication: \(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization